Question

Question #8f07d

Answer 1

`V= 36pi`

Explanation:

Consider the line:

`y= x/4`

For `x=12` we have `y=3`, so we can see that rotating this line around the `x`-axis in the interval `x in (0,12)` generates exactly the solid requested.

The element of volume generated by the cylindrical shell between `x` and `x+dx` is given by:

`dV = pi y^2(x)dx = pix^2/16dx`

so, integrating over the interval:

`V= pi/16 int_0^12 x^2dx = pi/16 [x^3/3]_0^12 = 36pi`