Question

There exists a 3-dimensional structure such that at height h the cross section is a square with side length 7sinh+7. If the height of the structure is 4π, then the volume of the structure can be expressed as aπ, where a is a positive integer. What is the value of a?

Answer 1

@waterineyes @AravindG @satellite73 @ganeshie8 @mathslover

Answer 2

@hartnn

Answer 3

@ash2326 @Mertsj @.Sam. @Callisto @amistre64

Answer 4

Volume = Cross section Area * height
here the cross section area is different at different height.
Let at height h, we consider a small height dh
the cross section area is
\[(7\sin h+7)^2\]
Do you understand this?

Answer 5

why square?

Answer 6

Square side is 7 sin h +7
so areas will be the square of the side

Answer 7

ok

Answer 8

so the volume will be
\[\int (7 \sin h +7)^2\times dh\]
height varies from 0 to 4pi
\[\int_{0}^{4\pi} (7 \sin h +7)^2\times dh\]
Can you do this integration?

Answer 9

what's the ans.?

Answer 10

i got 294

Answer 11

Yes, me too.

Answer 12

thanks

Answer 13

welcome :D