







An open top box 
20181212 

From Kirklan: Jeremy wants to construct an open box from an18inch square piece of aluminum. He plans to cut equal squares, with sides of x inches, from each corner and then fold each side up to form the box. If Jeremy wants the volume of the box to be 432 cubic inches, what should the minimum length of the sides of the squares cut from each corner be? Find the volume, V, of the box as a function of x. Given: V = length × width × height. Answered by Penny Nom. 





Filling a candy box 
20181016 

From Stephanie: My child had the question: A candy box has the following measurements.
10x6x4Find the total volume. (We got that one right 240in3)
But... then it said “How many 1/2 inch cubed pieces of candy can fit in the box?
This is where we disagree. Please help. Answered by Penny Nom. 





The distance between two men 
20180421 

From Kristin: If a 5 ft 6 in man gets hit at a downward 45 degree angle by a 5 ft 10 in man, how far apart are the two men? AND, would the shorter man have to be kneeling or standing? Is there a formula and answer for this question? Answered by Penny Nom. 





The length of a diagonal of a box 
20180413 

From Valentina: A packaging box for a metal rod is 7.5 inches along a diagonal of the base the height of the box is 18 inches what is the lengh of a diagonal of the box? Answered by Penny Nom. 





The volume of a box with a hexagonal base 
20160327 

From Frank: how many gallons of water in an 8" hexagon shaped box. 6" sides x 12.5" high ? The walls are 1" thick , beveled @ 30 degrees, so inside dimensions are 6" Answered by Penny Nom. 





A square based box and a cylinder 
20160326 

From rajpal: i m trying to calculate an area required to hold 4.4 mln cubic metres of volume.
I used square and I get below result
A box shape that has dimensions 1500 meters (1.5km) by 1500 meters (1.5km) by 2 meters depth has a volume of:
= 4,500,000 cubic meters (4.5 mln cubic meters)
but when I use a cylinder shape, i get below result
A cylindrical shape that has a radius of 850 meters and a depth of 2 meters has a volume of:
= 4,539,600 cubic meters (4.54 mln cubic meters approx)
why is it that the cylinder, though of same depth holds more volume than a square?
kindly clarify. Answered by Penny Nom. 





Building an 8 sided box 
20141014 

From Michael: I want to build an 8 sided box. The North, East, South, and West sides I want them to be 4 feet in length.
The NE, SE, SW, and NW sides I want to be 2 feet in length. What angles do I need to cut my angles.
Thanks Michael Answered by Penny Nom. 





A ball in a box 
20140209 

From kenneth: I have 2 questions.What is the radius of the largest ball that will fit into a box that has the inside dimensions of 6feet by 8 feet by 10feet. and the second question is how many cubic feet of concrete will you need to complete a patio that is 20 feet long by 15 feet wide by 5 inches in hight. Answered by Penny Nom. 





A boxandwhisker plot with one whisker 
20140109 

From Susan:
Question from Susan, a teacher:
I read your answer to the question about could a box & whisker have NO whiskers.
It made sense to me. However I am preparing for my advanced class and I have a sample graph comparing box plots of data.
Several of the box have only 1 whisker. There is no explanation for this. Can you help me out. I cannot think of a data set that would produce this. Thanks! Answered by Penny Nom. 





The popcorn box problem 
20131107 

From Dave: We know that calculus can be used to maximise the volume of the tray created when cutting squares from 4corners of a sheet of card and then folding up.
What I want is to find the sizes of card that lead to integer solutions for the size of the cutout, the paper size must also be integer. EG 14,32 cutout 3 maximises volume as does 13,48 cutout 3.
I have done this in Excel but would like a general solution and one that does not involve multiples of the first occurence, as 16, 10 cutout 2 is a multiple of 8,5 cutout 1. Answered by Walter Whiteley. 





A balance puzzle 
20130114 

From Emily: I'm stuck on this problem and feel that it can't work! The problem is: there is a door with a balance scale on it. In order to open the door, you have to use the 5 weights to balance the scale. On the left side you have 2 boxes to place the weights and on the right side you have 3. You're 5 weights are as follows: 1lbs, 2lbs, 3lbs, 4lbs, 5lbs. How do you place the weights so that the scale is balanced? Answered by Penny Nom. 





A sand box with 14 sides 
20120710 

From Tom: Want to build a sand box for a pool that is fourteen foot round wanted to make it in fourteen pieces of wood what angle would each piece be and how long would each piece be Answered by Harley Weston. 





An octagonal sandbox around a pool 
20120612 

From Linda: My pool is 15 feet across and it is round.
How do I measure to cut wood to build a sandbox around it? was thinking it will look like an octagon.
Thanks Answered by Harley Weston. 





A storage box with a slanted roof 
20120213 

From Sophia: Hi!
I have another problem.
The diagram shows a side view of a box which is used to store small logs of
wood for burning in a fire place. The slopping lid has an overhand of 15cm.
a) Calculate the total length of the slopping lid to the nearest cm.
b) When the lid is open above ground will the end of the lid be?
P.S. Please see attached. Answered by Penny Nom. 





Litres in a box 
20120209 

From vicky: how much litre water can be filled in a box of 12 inches *24 inches *12inches Answered by Penny Nom. 





The number of gallons in a box 
20111218 

From matt: i need to know how many gallons a 16 inch square box will hold Answered by Penny Nom. 





A lock box 
20110803 

From Tom: I need to open a lock box from my parent's estate. The combination is a simple 4 number lock. The last two numbers are 33. Numbers can be used more than once.What are the possible combinations?
WP Answered by Harley Weston. 





A cylinder fits perfectly in a box 
20110718 

From Brix: A cylinder fits perfectly in a box. 76 cubic inches of oil is poured into the space between the cylinder and the box, filling the space halfway. If the box is 3ft wide, how tall is the cylinder in inches? Answered by Stephen La Rocque. 





A punchcode lock box 
20101129 

From Doug: I am a real estate agent that uses punchcode lock boxes on houses to store the keys. I need to crack the code on one of our boxes, so I need a list of the possible combinations.
Rules:
4 digit code
Numbers 09
Each number can only be used once
Order of the numbers does not matter.
With advice from this site, I have calculated that there should be 210 possibilities.
10x9x8x7 (5040) gives me the total number possibilities and 4x3x2x1 (24) gives me the total number of ways to arrange those numbers.
So if I divide the possibilities by the arrangement, I get 210. (5040 / 24 = 210) GREAT!!!
Now, how do I develop a list of those 210 combinations?
Thanks for your help. Answered by Robert Dawson. 





A box full of oranges 
20101028 

From Mary: A box full of oranges weighs 9 pounds. After a family ate 2/3 of the oranges, the remaining oranges and the box weighed 4 pounds. The weight of the box when empty is how many pounds? Answered by Penny Nom. 





A collection of baseball cards 
20100701 

From Martha: Cody has a collection of baseball cards. Is it possible for him to
place the cards into 5 boxes so that exactly 3 of the boxes contain an
odd number of cards and the total number of cards in two of the boxes
is the same as the total number in the other 3 boxes? Explain. Answered by Robert Dawson, Penny Nom and Claude Tardif. 





What are the dimensions of the box? 
20100413 

From Steven: The longest rod that will just fit inside a rectangular box,
if placed diagonally top to bottom, is 17 inches.
The box is 1 inch shorter and 3 inches longer than it is wide.
How much must you cut off the rod so that it will lie flat in the
bottom of the container? What are the dimensions of the box? Answered by Robert Dawson. 





A rectangular box packed with cylinders 
20100316 

From Laura: There is a cylinder which has a diameter of 10cm and height of 10 cm. Work out the volume of the cylinder. Then in a packed box of 20 cylinders (height of box 10cm) work out the volume inside the box that is not filled by the cylinders give your answer in terms of pi. Answered by Penny Nom. 





What is the height of this box? 
20100219 

From Carol: A rectangular box with a volume 0.75 cubic meters, Length 1.5 meters and width 0.4 meters. What is the height of this box. Answered by Tyler Wood. 





The volume of a box 
20090415 

From Karen: Will 200 cubic centimeters of soil fit into the box?
8 CM by 6 CM and 4 CM deep Answered by Penny Nom. 





A rectangular open box 
20090321 

From tina: An open box is to be made from a rectangular piece of tin by cutting two inches squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin. Answered by Stephen La Rocque. 





What deminsions should my box be? 
20090219 

From Mary: My item is 57cm x 36cm x 6cm and I want to put 20 items is 1 box. What deminsions should my box be? Answered by Stephen La Rocque. 





A circular plaque in a square box 
20081128 

From kmart: A square box has a diagonal of length 640cm.It is to contain a circular wall plaque. What is the
approximate diameter of the largest wall plaque that can be placed in the box? Answered by Penny Nom. 





A cereal box that has a volume of 12000cm^3 
20081124 

From William: Hi, I have this math question that says construct a ceral box that has a volume of 12000cm3 and the surface area of the box has to be between 3200cm2 and 400cm2, I found some dimensions that are 20 by 20 by 30 and it works, but when I attempt to make the box, or make a net I would need this hugh piece of paper/cardboard, which I don't have, is there an easier way to find different dimenshions so I dont need a hugh piece of paper to create a net easily? Because i've tried trial and error but it has taken to long and I cant find anything,else, thats resonable. Answered by Harley Weston. 





The volume of a box 
20080916 

From Andre: volume of the box cubic centimeters
____ X _____ X ______ X =_______
The length is 8.5 Width is 3.4 Answered by Penny Nom. 





Volume of a Shed 
20080724 

From lou: I need to know the interior volume in cubic feet of a shed with the dimensions 8' x 10' x 7' with a roof peak of 9'. Thanks Answered by Janice Cotcher. 





Constructing An Open Box 
20080723 

From Rita: An open box with a square base is needed to have a volume of 10 cubic feet.
(a) Express the amount A of material used to make such a box
as a function of the length x of a side of the square base.
(b) How much material is needed for a base 1 foot by 1 foot? Answered by Janice Cotcher. 





Packing a truck 
20080610 

From Ann: I am renting a 24ft box truck and have been told it is 1401 cubic feet. I want to know if I have 23 display cases to move and each is 6ft X 2ft X 3ft will the all fit? Or do I need additional info in order to figure this out? Answered by Penny Nom. 





An open box 
20080423 

From Le: Metal Fabrication; If an open box is made from a tin sheet 8 in square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made. Answered by Harley Weston. 





The volume of a cereal box 
20080303 

From Lawson: I have calculated the volume of a box of cereal whose dimensions are:
Length  19 cm
Width  3 cm
Height  27 cm
I need help with the follow question:
If 2cm3 = 30 pieces of your cereal, how many pieces of cereal will fit in your box? What do I do the calculate? Answered by Penny Nom. 





Maximum volume of a box 
20080115 

From Rajesh: A square piece of a cardboard of sides ten inches has four equal peices are removed at the corners, then the sides are turned up to form an open box. What is the maximum volume such a box can have? Answered by Stephen La Rocque. 





The surface area of the rectangular solid 
20071230 

From Sara: For my math homework i found the volume of a rectangular solid whose deminsions were in feet and the numbers were 10 by 20 by 30
10 = hight
20 = short side base
30 = long side base
and now i have to find the surface area of the rectangular solid....
i know how to do this but i can't get the right answer
it should be 2,200 ft squared but i keep getting 13,00 feet squared Answered by Penny Nom. 





The dimensions of a box 
20071130 

From nephi: if i wanted to make a box that was 0.35 ~ 0.7 Cubic Feet on the inside how would i go about making the measurements for the outside? Answered by Penny Nom. 





Nine dots 
20070925 

From al: Connect the dots.
There is nine dots, three across and three down.
Connect the nine dot with the pencil only using four line and never lifting the pencil off of the paper. Answered by Stephen La Rocque and Harley Weston. 





Making a box with a particular volume 
20070620 

From Kimberly: How do you convert 487 cf into box? Answered by Stephen La Rocque. 





A boxandwhisker plot with no whiskers 
20070418 

From Paula: Is it possible for a boxandwhisker plot to have no whiskers? 3 whiskers? Answered by Penny Nom. 





An octagonal box 
20070331 

From eddie: I need to make one wood box in octagon type, that has 1125.00 square feet.
I want to know how many feet in one side Answered by Penny Nom. 





The volume of a triangular box 
20060912 

From Irene: How do I find the volume of a triangular box? Answered by Penny Nom. 





A 52 cubic foot box 
20060614 

From Konstanze: I need to figure out what LXHXW I need to create a 1.5 cubic meter or 52 cubic foot volumethere is an answer in your database that relates to this..but it does not give the formula to go from cubic feet/inches to a measurement for a box.
Empirically I can figure out that 3 x 3 x 3 equals 27 and that 3.5 feet (42") x 3.5 x 3.5 equals 42.87 and 3.75 x 3.75 x 3.75 equals 52.73 which is about 1.5 cubic meters (1cubic meter = 52.971643 cubic feet) i.e a box 45 x 45x 45 "
There must be an easier way. Answered by Penny Nom. 





A box with an interior of 1.26 cu. feet 
20060519 

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. 





A box with volume 0.78 cu ft 
20060510 

From Sherrina: i need to build a box that equals .78 cu ft any ideas on how i do this Answered by Penny Nom. 





Quarts, liters cubic yards and soil 
20060319 

From Kathy: I am trying to find out how many quarts of dirt there are in a yard of dirt. The local flower store sells bags of dirt that are 20 quarts or 22 liters for $1.25 and another store sells a yard of dirt for $25.00. Which is the better deal? Answered by Penny Nom. 





The dimensions of a box 
20060223 

From Ben: I need to find the dimensions of a rectangular box. They ask for the areas of the top, side and end. If those areas are 120 square units, 96 square units, and 80 square units respectively, what are the dimensions of the box? Answered by Stephen La Rocque. 





Stemandleaf plots, boxandwhisker plots and medians 
20060221 

From A student: explain which plot would be easiest to use to find the median....boxandwhiskers plot or stemandleaf plot Answered by Penny Nom. 





Outliers in a box and whisker plot 
20060219 

From A student: i need help on determining if their is an outlier...i know how to find the median and the lower quartile and the upper quartile..but i don't understand about the outliers....please tell me if their is an outlier in this problem....the numbers are...63,88,89,89,95,98,99,99,100,100 Answered by Penny Nom. 





A two cubic foot box 
20051027 

From Michael: I need to make a box that measures two cubic feet. It will be used to items in to determine if an inmate has to much property. They can only possess 2 cubic feet of property. How can I convert that into measurements in inches for feet so I can make a box with a lid that is 2 cubic foot. I sure hope you can help me Answered by Penny Nom. 





Cubic yards is in a box trailer 
20050920 

From barbara: i need to know how many cubic yards is in a box trailer that is 96" wide 13' 6" high and 40" long Answered by Penny Nom. 





Volume of a box 
20041118 

From Catherine: I need to find a formula to calculate the amount of liquid would hold. maybe the volume or something. its a square box used to hold liquid on a farm . we want to measure how much liquid it can hold. Answered by Penny Nom. 





A travelling salesman 
20040909 

From Liz: A salesman traveled due west from city A to city B. The distance he traveled, that is the ditance from A to B, was X miles. He returned from B to A and found that he had traveled half the distance, X/2 miles. How can that be? Answered by Chris Fisher and Penny Nom. 





What is the name of a 3D rectangle? 
20040607 

From Jack: if a cube is a 3D square, what is the name of a 3D rectangle? Answered by Penny Nom. 





Volume of a box 
20040523 

From A student: The area of the top of a closed rectangular box is 252cm2, the area of the front of the box is 105cm2, and the surface of the box is 834in2 (or 5380.64cm2). What is the volume of the box? Answered by Penny Nom. 





The combinatiion for a keybox 
20040517 

From Darrin: I have a puzzle question based on reality. I have a realestate type keybox (Supra) that has 10 digits, 09. I am trying to figure out a methodical way to test all number combinations to it to open it. (totally legal it was taken from the trash at a jobsite since they couldn't open it!) The combination could be any or all of the digits, but any digit is only used once. This is not like a simplex lock problem where a combination of keypresses would be different i.e. 1,2,3 is the same as 1+2,3.
Any ideas? Answered by Penny Nom. 





Four marbles on a box 
20040322 

From Karyn: Suppose 2 solid color marbles and 2 striped marbles are placed in a box. All are the same size. If one marble is randomly drawn from the box and replaced, then a second marble is randomly drawn, what is the probability that the marble drawn both times will be striped?
I know there is a simple formula for working this out but I can't remember how.
Answered by Penny Nom. 





Distributing r identical balls into n distinct boxes 
20030316 

From Diana: How many ways to distribute r identical balls into n distinct boxes with exactly m boxes empty? Answered by Penny Nom. 





The dimensions of a box 
20021203 

From Paula: My son, who is in secondary school, needs to make a box with the inside dimensions of 1.25 cubic feet. It's supposed to be more in the shape of a rectangle than a square. I would like to know the equation to use to find the inside dimensions of a box if I know how many cubic feet (or inches) I need the inside to be. Answered by Penny Nom. 





A box that holds 22.4 liters 
20020707 

From Jon: How do I find the measurements required to make a box that holds 22.4 liters of something? Answered by Penny Nom. 





Box and Whisker plots 
20011119 

From Rod: In our Prealgebra course, we have been studying Box and Whisker plots. Recently, we learned how to decide whether a data point is an outlier or not. The book (Math Thematics, McDougall Littell) gave a process by which we find the interquartile range, then multiply by 1.5. We add this number to the upper quartile, and any points above this are considered to be outliers. We also subtract the number from the lower quartile for the same effect. My question: where does this 1.5 originate? Is this the standard for locating outliers, or can we choose any number (that seems reasonable, like 2 or 1.8 for example) to multiply with the Interquartile range? If it is a standard, were outliers simply defined via this process, or did statisticians use empirical evidence to suggest that 1.5 is somehow optimal for deciding whether data points are valid or not? Answered by Penny Nom. 





A box of pants and shirts 
20011117 

From Debbie: I need to determine the volume of a box that is 4'HX4'WX4'L. The box contains uniform pants and uniform shirts. I need to know how many shirts and pants are in the box. When folded, the uniform shirt is .5 inches thick. The pants are also .5 inches thick. Answered by Penny Nom. 





A box with an interior of 1.25 cubic feet 
20010326 

From Gabe: I need a box with an interior of 1.25 cubic feet. I am using 3/4 inch material to make the box. What would the exterior dimensions be in inches? Answered by Harley Weston. 





The repetend in repeating decimals 
20010321 

From Sharon: What is the name for the bar over the repetend in repeating decimals? Also, what is the name of the long division "house"? Answered by Penny Nom. 





The "goesinta" box 
20010207 

From Bridget: We are looking for the "proper" name of the "box" that is drawn around the dividend on a division problem: ___ 3)12 It has always been a family joke to call it the "goesinta" box, but a search of several reference sources hasn't yielded an answer  This is a question of curiosity rather than a question for homework. Answered by Claude Tardif. 





Volume of a box 
20001115 

From A student: A box 3" wide and 2" deep is to have a volume of 2 cubic feet. How long must the box be? How many pieces of lumber are stacked in a pile 2" high if each board is 3/8" thick? Answered by Penny Nom. 





Box and whisker plots 
20000309 

From Brett Blake: Do you have any information on Box and whisker graphs? Answered by Harley Weston. 





Three dimensional rectangle 
20000111 

From Dennis Murphy: I would like to find out the name of a Three dimensional rectangle. Answered by Harley Weston. 





Probability 
19980917 

From Chris: Six marbles are placed in one of three boxes. What is the probability that each box contains two marbles? What is the formula used? Answered by Penny Nom and Chris Fisher. 

