Calculus volume question I can't figure out,

Question

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. 
y=x^2, y = 0, x = 0, x = 3, about the y-axis

Answer 1

The area of the region is bounded by y = x² and y = 0

As the specified curve is about y axis then convert the x terms into y.

y = x² ⇒ x = √y

If x = 0 then y = 0

If x = 3 then y = 9

Then area of the region A(x) = πx² = π(3² - (√y)²)

Now volume of the region is .

Therefore the volume of the region is 81π/2.