







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. 





Cutting a hexagon from a disk 
20140405 

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 
20120111 

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 xaxis 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 
20100918 

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 
20080428 

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 
20070408 

From christina: find the volume of the solid formed when region bounded by y=x/3, y=2
and the yaxis. it is revolved about the xaxis.
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 nonrerctangular lot 
20050118 

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 
20031029 

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 
19980829 

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 xaxis. 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 xaxis. Thanks. Lorraine Answered by Harley Weston. 





Volumes of Revolution 
19980724 

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 xand yaxes, 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 yaxis using the shell method but I can't seem to be able to get started with the volume when rotated about the xaxis. Answered by Harley Weston. 

