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 Topic: cube
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How many cubes are in a 3x3x3 cube? 2019-06-24
From Darren:
Dear Sir/Madam, How many cubes of different sizes (eg. 1x1x1, 2x2x2, 3x3x3) are there in total in say, a 3x3x3 cube? I have trouble figuring this out.

Yours faithfully,
Darren

Volume and Surface area of a sphere 2019-05-03
From Caitlin:
Why does the surface area formula of a sphere have a squared radius while the volume of a sphere has a cubed radius?
A puzzling equation 2018-12-04
From Manny:
Hello,

Can you explain why this is wrong:
-1 = (-1)^3 = (-1)^{6/2} = ((-1)^6)^{1/2} = (1)^{1/2} = 1 ??

Thank you

A cube in a cylinder 2018-08-13
From Geli:
A cylinder with a radius r and height 2r+4 contains a cube with edge length r√2. What fraction of cylinder volume is taken up by the cube
A triangle in a cube 2018-04-16
From Sohel:
A cube has an edge of 4 cm. A triangle is formed by joining the middle point of one face of the cube to the ends of a diagonal of the opposite face . What will be the area of the triangle ?
The volume of a cube 2018-03-15
From Eli:
An outdoor art display is a metal cube with edge length 39 feet. What is the volume of the cube in cubic​ feet? In cubic​ yards
The diagonals of a cube 2016-12-02
From Peter:
when u have a cube and the inner diagonal is 41.6 how long is the outside diagonal
A cylinder in a cube 2016-05-25
From Sonia:
A cylinder has the same height and diameter as the sides of a cube use 3.14~ which has the greater volume
The volume of a cube 2015-04-30
From megan:
What's the volume of a cube with a side length of 6?
A limit 2015-02-19
From genc:
Lim (27x^3-1) / (3x-1)
X-> 1/3

A difference quotient 2015-01-12
From Sasha:
Simplify the difference quotient

f(x) − f(a)/ x-a
if x ≠ a.
f(x) = x^3 − 12

The cube root of 729 2014-11-12
From Alexis:
What would be the square root of 729 to the third power and could you explain how to get the answer?
The diagonals of a cube 2014-09-04
From Rukshanth:
How many diagonals does a cube have?
Five cubes 2014-01-15
From Bob:
Rick has five cubes. When he arranges them from smallest to largest, the difference between the heights of any two neighbouring cubes is 2 cm. The largest cube is as high as a tower built from the two smallest cubes. How high is a tower built from all five cubes?
Tesseract 2013-08-22
From Dan:
I am not a mathematician. This seems to me an intuitively simple enough problem that I very much need an answer to from someone who's mathematics are better than mine. Please help.

The question is: for a tesseract of side length = 1 what is the distance of the center of each cube from the center of the tesseract ?

I think I have calculated the distance of each vertex from the center, and of the center of each edge from the center, but the question above baffles me.

(anyone not having a clue what I am talking about can brush up here http://en.wikipedia.org/wiki/Tesseract )

Thanks in advance - Dan V

Squares and cubes 2013-08-02
From Sandra:
What whole number equals 25 when it is squared and 125 when it is cubed?
a cube-b cube-a+b= ? 2013-06-16
From saryu:
a cube-b cube-a+b= ?

Every vertex of a cube is assigned a number +1 or -1 2013-04-01
From Shankar:
Every vertex of a cube is assigned a number +1 or -1 . Every face has a number that is the product of all the numbers in its corners. Then the 14 numbers are summed up ( all the vertices and faces ). Can the sum be 0?
Two cubes 2012-09-04
From alexis:
a cube has one face that is equal to the total surface area of another cube. Find the ratio of their volumes
A cubical tank 2012-07-07
From jake:
a storage tank is in the form of a cube. when it is full of water,the volume of water is 15.625 m cube. if the present depth of water is 1.3m, find the volume of water already used from tank
Three metallic cubes 2012-05-13
From Pragun:
Three metallic cubes whose edges are in the ratio 3:4:5 are melt to form a single cube whose diagonal is 12*square root of 3. What are lengths of the edges(in cm) of the three cubes
A cube inscribed in a sphere 2012-01-23
From Gelo:
What are the largest volume and total surface area of a cube that may be inscribed inside a sphere whose radius is 5 kilometers.
The number of gallons in a box 2011-12-18
From matt:
i need to know how many gallons a 16 inch square box will hold
A cube of ice is melting 2011-12-05
From Emily:
a cube of ice (i.e.) each side is of the same length) is melting at a rate such that the length of each side is decreasing at a rate of 5cm per hour. how fast is the volume of the cube decreasing (in cubic cm per hour) at the instant the length of each side is 25cm?
A pattern is built with cubes. 2011-02-08
From e:
A pattern is built with cubes.
The first item is 1 cube.
The second item is a block of 8 cubes.
The third item is a block of 27 cubes.
If the pattern is continued, how many cubes are needed for the fourth and fifth?

Determine if a point is inside a cube 2010-11-24
From Ali:
hi every one i have a problem with cube they told me to write a program that determine if a point is inside a cube so i need the equation of the cube to do the comparison. in sphere it is easy sqrt((x-xp)+(y-yp)+(z-zp))<=radios if u please could help me
Difference of cubes 2010-05-22
how can we prove a^3 - b^3 is equal to (a-b)(a^2+ab+b^2)?
A cube with twice the volume 2010-04-11
From Woojin:
From a given cube create another cube with twice the volume. the cube: 5cm each.
1^3 + 2^3 + 3^3 +4^3 ... n^3 = ? 2010-01-29
From ireimaima:
Hi..
Can u please help me with this question.. I find that when i test eg: n=2 for n (n+1) /4, it seems that it does not giving me the right answer of 1^3 + 2^3 = 9 but 3/2... i'm confuse..can u please help me..thanks so much

Prove that: 1^3 + 2^3 + 3^3 +4^3..n^3 = n (n+1) /4

The cube of an integer 2010-01-20
From Shankar:
Can the cube of an integer end with 1985 ones ?
Cubes and squares 2009-09-16
From Stanley:
What is a three consecutive digit number like 5,6,7 , which is two less than a cube and two more than a square?
A difference quotient 2009-06-17
From Sue:
When s(x)=x^3+x, compute and simplify the difference quotient s(x+h)-s(x)/h.
Constructing a cube 2009-04-08
From Jill:
you have a sheet of cardboard that measures 9ft x 6ft. To make the entire sheet into a closed box tht is a perfect cube, what would be the surface area of the box?
Surface area of a cube 2009-02-22
From JOHNNIER:
determine the surface area of a cube with volume 125 mm3, thank u very much
The surface area of a cube and rectangular prism 2009-02-16
From Mhiko:
how to derived the total surface area of a cube and rectangular prism using geoboard??
Solid figures 2009-02-10
From Rebecca:
I need to know the names of solid figures. I have several pictures that I need to answer what type they are. Thanks, Rebecca 3rd grade
Ratio of Volumes of a Cylinder and a Cone 2008-12-06
From rohan:
A CYLINDER IS WITHIN THE CUBE TOUCHING ALL THE VERTICALS FACES . A CONE IS INSIDE THE CYLINDER.IF THEIR HEIGHT ARE SAME WITH SAME BASE ,FIND THE RATIO OF THEIR VOLUMES.
Factoring 2008-11-19
From Neji:
How do you factor (y-z) (y+z) (y^4+y^2z^2+z^4) and get (y+z)(y^2-yz+z^2) (y-z) (y^2+yz+z^2) as the answer?
Balls and cubes in an urn 2008-09-09
From Dave:
In an urn, there are 80 objects of two kinds: cubes (C) and balls (B). An object can be either red (R) or green (G). Note that all the four combinations are possible and that the number of cubes is not necessarily equal to the number of balls. Similarly, the number of red objects is not necessarily equal to the number of green objects. Someone tells us that in the urn there are 20 red cubes, 50 balls, and 30 red objects. An object is randomly selected from the urn.
(a). What is the probability that a green ball is selected?
(b). If we know that a cube has been selected, what is the probability that it's red?
(c). If we know that a red object has been selected, what is the probability that it's a cube?

Hidden Faces of a Row of Cubes 2008-08-25
From Mhiko:
how many hidden faces of a cubes are there in a 5 cubes in a row? how many hidden faces of a cubes are there in a 10 cubes in a row? how many hidden faces of a cubes are there in a 15 cubes in a row? how many hidden faces of a cubes are there in a 20 cubes in a row? please show me the solution or formula....
A cubic equation 2008-08-25
From RAM:
The following Cubic Eqn should have three roots - what are they?

x^3-27=0

The cube root of a really big number 2008-07-17
From Pete:
Is the only way to find a cube root of a really big number guess and check, as i read in other questions, or is there another way without a calculator?
A cube inscribed in a right cone 2008-07-16
From Steven:
A cube is inscribe in a right cone of radius 2 and height 5. What is the volume of the cone?
Answered by Victoria West and Harley Weston.
The surface area of a cube 2008-05-24
From cailtlin:
hi.. if the surface area of a cube is 384 cm^2, how could i find the length of one edge? thank you
The cube of -2y in exponential form 2008-05-19
From Xiu:
I dont get this question.. Write "the cube of -2y" in exponential form. I know the answer is -(2y)^2 but i really don't understand why. Can you explain how to do this whole problem for me?
The cube root of 198 2008-03-27
From bobby:
what is the cubed root of 198
The surface area of a cube and a cylinder 2008-03-16
From sunday:
I'm doing a unit assessment, and there is something I don't understand. Now in my textbook, it says that surface area for a cube is different from a cylinder. Surface area for a cylinder has two numbers, but surface area for a cube has 3 or more numbers. And plus, I can't figure out the volume for a cube because it only shows volume for a cylinder. So how do I get this right?
Estimate the cube root of 270 2008-03-11
From Tom:
(a) By plotting suitable graphs, estimate to one decimal place the cube root of 270.
(b) With reference to your answer to part (a), use 8 iterations of a Bisection Search to refine your estimate. Use the nearest whole numbers either side of your estimate from part (a) as starting values.
(c) Using either of your starting values from part (b) as first guess, use the Newton-Raphson method to find the true value of the root (to 6 decimal places). Repeat using the other starting value from part (b) and compare the two results.

The cube root of 103163 2008-02-12
From jeff:
find the cube root of 103163
Answered by Stephen La Rocque and Harley Weston.
The diagonal of a cube 2008-02-10
From Praveen:
Given a Cube's diagonal, how does one find the edge of the cube.
Sum and difference of cubes 2008-01-30
From Amanda:
It has been a really long time since I was in Algebra and I can't remember how to factor cubes such as x^3 +81 or subtracting/adding fractions with variables such as [1/(x+h)+2]-[1/x+2]. Please help!!!
Explaining the factoring for the difference of cubes 2008-01-16
From Bill:
A student asked me where did the "difference of cubes" and "sum of cubes" come from. I did not have an answer for her. She is very bright and understands how they work but wanted to know where they derived from. Any help you can offer would be great. Thanks
The cube of a number 2008-01-12
can you help me to find out how to cube a number example (6 cubed / by4) =54 what is cube or how do you cube something
What length of hose will I need? 2008-01-03
From Justin:
I have one cubic yard of liquid that I want to convert to a cylindrical volume with the inside dimensions being 3/4 of an inch. I am trying determine what the height/length would be to set these equal. i.e. What length of hose will I need (with an inside diameter of 3/4") in order to accommodate exactly one cubic yard of liquid?
How many cubes have one face painted red? 2007-11-27
From Ashutosh:
A rectangular block measuring 10 units by 8 units by 6 units is made up of cubes measuring 1 unit on a side. The base of the block is 10 units by 8 units. The outside of the block other than the base is painted red. How many of the unit cubes have exactly one face painted red?
Answered by Stephen La Rocque and Penny Nom.
Cubes 2007-09-21
From Yvonne:
The numbers 756 and 72, expressed as products of prime factors, are 756 = 2² x 3³ x 7 and 72 = 2³ x 3²

Use these result to find,

the smallest integer, x, such that 756x is a perfect cube.

A cube in a sphere 2007-09-11
From Justin:
What percent of the volume of a cube is occupied by the largest possible sphere centered in that cube?
Find all numbers which are both squares and cubes 2007-07-30
From Arul:
what is the easiest way to find the number which is both a square and a cube? the numbers i know are 64 and 729 which is both a sqr and a cube. i took long time to solve this.. is there any easier way?
The volume of a cube 2007-06-23
From Leah:
I am having trouble finding the equation for this problem.: What is the volume of a cube with diagonals of length 6 sqrt(3) cm? answer: (BLANK) cm3
I am filling a hole in the shape of a cube 2007-04-11
From Bethany:
If I am filling a hole in the shape of a cube with 64 cubic yards of dirt, how many feet deep will my hole be.
The cube root of 8000 2007-01-31
From Jacqui:
How would you find the answer of a cube root backwards. For example: 8000 but backwards. Like, what number made that and how would you do it?
Drilling holes in a cube 2006-12-12
From Liz:
What is the volume of the solid remaining if a unit cube has a hole drilled thru one face to the opposite side and the hole that is drilled is a cylinder of unit diameter. Then the cube is rotated and an identical hole is drilled from an untouched face to the opposite side. Then the cube is rotated and an identical hole is drilled between the last two untouched faces. This will result in the cube vertices and the remaining volume of the cube falling into 8 parts. What is the total volume of these 8 parts. How is this volume calculated?
A trillion sugar cubes 2006-11-10
From Leeza:
How many dump trucks (I believe the standard bed size is 16'L x 8'W x 4'D) would it take to hold one trillion sugar cubes (which I believe are approximately 2cm in L, W and D)?
A sphere in a cube 2006-11-09
From Lukas:
Given a cube and a cross diagonal, what is the largest size sphere that fits in the cube and does not touch or intersect the cross diagonal?
Answered by Steve La Rocque, Penny Nom and Walter Whiteley.
(a^(1/3)  b^(1/3)) ( a^(2/3) + a^(1/3)b^(1/3) + b^(2/3)) 2006-10-24
From Julie:
(a1/3  b1/3) ( a2/3 + a1/3b1/3 + b2/3)
The volume of a cube 2006-09-29
From Greg:
Nicolai said that 6 billion can represent the volume of a cube. How many units long is the cube? How do you know?"
A cube inscribed in a sphere 2006-08-03
From Glenn:
Given the diameter of the sphere 10cm. find the largest cube inscribe in the sphere.
A box with an interior of 1.26 cu. feet 2006-05-19
From Maria:
I am trying to build a box with an interior of 1.26 cu. feet with all sides equal.
Answered by Stephen La Rocque and Penny Nom.
How many of these cubes have no wax of them? 2006-03-10
From Iban:
cube cheese is 4cm wide, 4cm long, 4cm high. three faces of the cube meet in the corner covers thin layers of wax. The cheese is then cut two, then cut 64 small cubes, which is the length 1cm. How many of these cubes have no wax of them?
Factor 2006-03-08
Factor:
x3 + 64m3 and 125p3 - q6

3x^4 - 81 2006-01-02
From Julio:
How can I factor the following?:

3x4 - 81

A cube in a sphere 2005-10-19
From Damian:
A sphere passes through the eight corners of a cube side 10cm. Find the volume of the sphere.
A diagonal in a cube 2005-03-06
From Brett:
A cube has a volume of 64 cubic inches. What is the length of segment AB? Segment AB is a straight line from the top left corner of the cube to the lower right bottom corner
The side of a cube 2005-01-17
From Jake:
I have one for you that's got me stumped. Is it possible to calculate the dimensions of a square if I have the cubic feet? Say I know the package to be 180 cubic feet.
252 x ? is a cube 2004-12-22
From Andrea:
What is the smallest positive interger by which 252 can be multipled so the result is a perfect cubed?
"a" cubed minus "b" cubed 2004-12-02
From Denise:
"a"cubed minus "b"cubed equal (a-b) times
("a"squared plus "ab" plus "b"squared)?

I know this is a formula, but why is it true?

Slicing cubes 2004-11-23
From Anthony:
You are working with a power saw and wish to cut a wooden cube 3-inches on aside into 27 1-inch cubes. You can do this by making six cuts through the cube keeping the pieces together in the cube shape. Can you reduce the number of necessary cuts by rearranging the pieces after each cut?
Cube roots 2004-10-26
From A parent:
How do you solve the problem of finding the cubed root of (17 to the power of 3).
Can you show me each step and if you have a visual representation of this it would be very helpful.

Also can you show a step by step of finding the cubed root of 27. Visuals help a lot

A cube is inscribed inside a sphere 2004-08-18
From A student:
A cube is inscribed inside a sphere with radius sqrt8cm. Find the
(a) length of the cube
(b) volume of the space inside the sphere but outside the cube.

Factoring 2004-07-19
From A student:
Factor completely:
3x3 - 24y3
54x6 + 16y3
16xy - 4x - 4y - 1
0.09x2 - 0.16y2

What is the name of a 3D rectangle? 2004-06-07
From Jack:
if a cube is a 3D square, what is the name of a 3D rectangle?
Factoring 2004-04-27
From Bipin:
FACTORISE:

a to the power of 6 + b to the power of 6

Some factoring problems 2004-04-15
From KJ:

Factor these:
x3+125 -----> (x+5)3
8x3-27 -----> (?)
x2+36 -----> (x+6)2
x4-5x2+4 --> (?)

The volume of a cube 2003-11-22
From A student:
i have a cube, and the line that cuts threough the middle of the cube across to the other side is 4 radical6. what is the volume of the cube?
The surface area of a cube 2003-04-07
From Sarah:
if the volume of a cube is 64 cm, then what's the total surface area? I also want to know how to show my work.
Factoring 2002-12-11
From Larry:
Question:

how do u factor trinonmials

EX: X 3 + Y 3

X 3 - 8Y 3

8X 2 - 72

64A 3 - 125B 6

Factor completely 2002-11-21
From Shelley:
these two questions are to be factored completely but i have no idea how to factor them
1. (x-4y) 2 - 3(x-4y) - 4
2. x 6 + y 6

Two cubes 2002-07-12
From Vanessa:
The edges of a cube are 50% as long as the edges of another cube. What percent of the volume of the larger cube is the volume of the smaller cube?
Cube roots 2002-03-26
From Kathy:
My son is in 4th grade and needs to simplify the cube roots of 216, 512 and 64. How does he do this with a regular calculator or without?
24x^4 + 3x 2002-03-18
From gary:
24x 4 + 3x
The number of hidden cubes 2002-02-05
From Katie:
This problem is about finding the number of cubes visible and hidden in a cube.

In a cube that is 3x3, 19 cubes can be seen. 8 are hidden.
In a cube that is 4x4, 37 cubes can be seen. 27 are hidden.
In a cube that is 5x5, 61 cubes can be seen. 64 are hidden.
In a cube that is 6x6, 91 cubes can be seen. 125 are hidden.

The question is:
Explain how you could find the number of small cubes that are visible and hidden in a cube of any size.

Answered by Paul Betts and Penny Nom.
A hypercube 2001-11-20
From Ace:
Can I get a picture of a hypercube
Some algebra 2001-10-15
From James:
I cannot figure these out I was wondering if you could help me? I have no one to answer my questions.
1. (7x2  3yz)2  (7x2 + 3yz)2

2. Use Pascals triangle to expand (2x  y)4

3. 8x3 y - x3 y4

4. (m + 3n)2  144

5. 12x4 y  16x3 y2  60x2 y3

6. p3 q2  9p3 + 27q2  243

Combien 1.0 ml fait en metre cube 2001-09-10
From M. Mauger:
Bonjour, je voudrais savoir combien 1.0 ml fait en metre cube.
Cube roots on a calculator 2001-03-24
From Will:
Hi my name is Will.I have a question about the calculator TI-83 Plus or the use of a scientific calculator. It is about using them to turn a cubed root to a decimal. When using that for a rational and irrational number. Rational numbers is a number that terminates or repeates. A irrational number goes on and on and uses ... (like pie). Like when you type the cube root of 8 it gives you 2, and that is a rational number. The squre root of 2 is 1.41421356... that is irrational. So why is it when you put the cube root of 16 in the calculator it says 2.5198421 that is rational it terminates at the ninth digit and my float is set for the tenth? But why when you do it by hand you get the 2 times the cube root of 2 and that is irrational? Why is that?
From Nikki:
3) squareroot of x2 + 10x + 25

4) sixthroot of (m + 4)6

5) cuberoot of -64r6w15

.
.
.
.

Exponents 2001-01-14
From A student:
I am wondering if a number raised to the second power is "squared" and a number raised to the third power is "cubed" is there a name for any number raised to any other power.
The sum of the cubes is the square of the sum 2000-10-10
From Otoniel:
Without using mathematical induction, or any other method discovered after 1010 a.d. , prove that the sum of i3, (where i, is the index of summation) from one to, n, is equal to ((n*(n+1))/2)2
Five times a cube equals three times a fifth power 2000-07-05
From Harman Chaudhry:
Which is the smallest 10-digit number to be five times the cube of one number and also three times the fifth power of another?
Graphing cube roots 2000-04-27
From Heather Jones:
What do the graphs of cube roots look like?
Factoring ^6 2000-01-03
From Athena:

my name is Athena and I have a question on factoring: how would you figure this out:

(x6-y6) and (x6+y6)

towers of cubes 1999-10-05
From Sanker:
I need help to solve this Rules for bulding towers of cubes
 rule 1 The number of cubes on the bottom layer is always one less than the number of squares on the grid rule 2 Each new layer is made with one cube less than the layer underneath it.
1. Investigate how many different arrangements there are of 4 cubes on top of 5 cubes on a two by three grid

2. investigate the number of different arrangements of six cubes on top of seven cubes on a two by four grid

3. investigate the relation between the number of arrangements of cubes and the size of the grid
• when there are two layers of cubes
• when there are more than two layers of cubes

The sum of the cubes is the square of the sum 1999-08-25
From Bernard Yuen:
How to prove 13 + 23 + 33 + 43 + ... n3 is equal to (1+2+3+...n)2? (for n is positive integer)
Measuring the fourth dimension 1999-06-07
From Suzanne Hall:
Hi! The other day, two of my students asked a very interesting question: Is the fourth dimension measured with hypercubes? Their reasoning went like this: Lines are 1D and are measured with line segments, which are part of a line. Planes are 2D and are measured with squares, which are part of a plane. Space is 3D and is measured with cubes, which are part of space. So, logically, hypercubes would be used to measure the fourth dimension.
Volume of a cube. 1999-04-04
From Alex Elkins:
How do you find the volume cubic matter of a cube or space, example how many cubic feet in an example 6" high 4' X 6' rectangle

Thank You

Factoring 1999-03-30
From Maggie Stephens:
I don't know anything about factoring would you plese help me.

3x4 - 48

54x6 + 16y3

125-8x3

12x2 - 36x + 27

9 - 81x2

a3 + b3c3

Patterns 1999-01-07
From Melis Kalay:
I'm confused about questions like these:

1. 2by2by2 cube:

If this cube was painted blue on the outside,

• how many cubes would have 3 blue faces
• 2 blue faces
• 1 blue face
• 0 blue faces

Answered by Jack LeSage and Penny Nom.
Platonic Solids Surface Area 1998-12-02
From Rachel Bidwell:
How do you find the surface area of the 5 platonic solids, when they each have a volume of one cubic inch