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A square based box and a cylinder 2016-03-26
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.
Cutting a hexagon from a disk 2014-04-05
From Paul:
I am a machinist and sometimes need to make a hex from round material.
If I know the distance of the flat sides opposite one another of my hex, how can I calculate the size of material I need to turn to give me the right diameter to finish the part with six sides?

Answered by Penny Nom.
A volume of revolution 2012-01-11
From john:
find volume of solid generated by revolving the region in the first quadrant bounded by the curve y squared=x cubed, the line x=4 and the x-axis about the line y=8. The answer in the back of the book is 704 pi divided by5
Answered by Penny Nom.
May Lee's cake 2010-09-18
From Wafa:
May Lee bought a cake which is circular in shape. Her sister ate a quarter of the cake. Given that the area of the top surface of the remaining portion is 520 square cm, find the diameter of the cake.
Answered by Penny Nom.
A bowl is the shape of a hemisphere 2008-04-28
From josh:
a bowl is the shape of a hemisphere with diameter 30 cm and water is poured into the bowl to a height h cm. how do i find the volume of the water in the bowl
Answered by Harley Weston.
A volume of revolution 2007-04-08
From christina:
find the volume of the solid formed when region bounded by y=x/3, y=2 and the y-axis. it is revolved about the x-axis.

the assignment was to use both the washer method and the shell method but when i solved for the volume, i got different answers. i think my shell method is wrong because i know i'm having difficulties with using "dy" instead of "dx" here's my work so far:

Answered by Penny Nom.
A non-rerctangular lot 2005-01-18
From EM:
One corner of a 60X120 foot lot, otherwise rectangular, is a curve with a radius of 20 feet and a central angle of 90 degrees. What is the area?
Answered by Penny Nom.
A rectangle on a disk 2003-10-29
From Arthur:
How do I go about solving the following problem: What is the width of the largest rectangle with a length of 16 inches you can cut from a circular piece of cardboard having a 10 inch radius?
Answered by Penny Nom.
Volumes 1998-08-29
From Lorraine Wall:
Consider the region in the first quadrant bounded by the x and y axes, the vertical line x=3 and the curve y = 1 / (x squared + 3). Determine the volume of the solid by rotating this region about the x-axis. Now that is the first part.
I then have to find the coordinates of the centroid of the solid by rotating this region about the x-axis.

Answered by Harley Weston.

Volumes of Revolution 1998-07-24
From Lorraine Wall:
I'm on the section fpr The Computation of Volumes of Solids of Revolution and the following question is giving me problems:

-Consider the region in the first quadrant bounded by the x-and y-axes, the vertical line x=3, and the curve y=1/(xsquared + 3) I can determine the volume of the solid by rotating the region about the y-axis using the shell method but I can't seem to be able to get started with the volume when rotated about the x-axis.
Answered by Harley Weston.




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