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My answers for 2 and 3 got marked wrong, why? Problem Six (9 pts) Using the method of slices, show that the volume of a
My answers for 2 and 3 got marked wrong, why?
Problem Six (9 pts) Using the method of slices, show that the volume of a pyramid with a height of H MOS and a rectangular base with side lengths W and L has the volume V = }WLH. 1. Draw a sketch of the object providing labels for all key quantities (in other | V= 211 ) (Radius) (height) dx words H, W, and L). Draw a typical slice. (3pts) W 2. Write V in terms of an integral over the area of each slice. (2pts) V= 21 (( J WL) (H) dx = 2 1 (3 WL) (H) ]& 3. Determine how the area of each slice varies with height and find V. (4pts) A = b.h A= 20/ ( W. H ) { JX = 20 [ ( W .H ) 2 )2Problem Eight (10 pts) Start From: (x - R)'+y=r Useful Formula: (atb)2 - (a-b)] = 4ab 1. Using either MOD or MOS. find an integral formula for the volume of the torus in the figure. DO NOT TRY TO DIRECTLY EVALUATE THE INTEGRAL (6 pts) V= 20 / ( r) ( R) dx = 2TY [ ( ( ) ( R ) ]+ C 2. Interpret (and explain your interpretation) the integral in the first part of your answer as the area of a geometric region so that you can find the integral and thus find a formula for the volume of the torus in the figure. (4 pts)Step by Step Solution
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