solid formed

Question

Which of the following statements is true? The volume of the solid formed by rotating the region bounded by the graph of y = x2, x = 3, y = 0 around the y-axis is (2 points)

Answer 1

A thin washer has outer radius R = 3, inner radius x, and thickness dy.

 

So we must integrate (from y=0 to y=9)    (pi)(3²-x²)dy

 

That (integrand) can be rewritten             (pi)(9-y) dy     of which the antiderivative is   pi(9y - y²/2);

when we plug in upper limit 9 we get 81pi/2 and and when we plug in y=0 there's nothing else,

so final answer is (81/2)pi.