Find the volume V of the described solid S.
The base of S is a circular disk with radius 5r. Parallel cross-sections perpendicular to the base are squares.

Question

Find the volume V of the described solid S.
The base of S is a circular disk with radius 5r. Parallel cross-sections perpendicular to the base are squares.

kkutie7 · Answer

A=pi(radius)^2 ?

kkutie7 · Answer

this is calculus so i doubt its that easy

rational · Answer

a rough sketch might help
draw a circle of given radius and try to visualize the cross sections perpendicular to this circle

aum · Answer

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rational · Answer

the cross sections will be in another dimension that shoots out of this screen

kkutie7 · Answer

I follow so far

dumbcow · Answer

@aum, isnt
$$AB = 2 \sqrt{25r^2 -y^2}$$

rational · Answer

$$\large V = \int \limits_{-5}^5 \pi (2x)^2 dy$$


$\large  x^2+y^2 =  5^2$

dumbcow · Answer

@rational , there is no "pi" because its only looking at area of the square

rational · Answer

Ahh yeah will fix it :)

$$\large V = \int \limits_{-5}^5  (2x)^2 dy = \int \limits_{-5}^5  \left( 2\sqrt{25-y^2}\right)^2 dy $$

rational · Answer

does that look okay, 
i deliberately removed r as i thought radus is 5 and not 5r

kkutie7 · Answer

so your are using the radius as a sort of x values here from -5 to 5 and the function its the horizontal line of the cross-section?

rational · Answer

the volume element here is a square of very thin radus
the side of the square is  2x and you can only see top view in below picture :

|dw:1411706452217:dw|