← Back to Test

Problem 18 - Entrance Test

Find the volume of the solid generated by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.

Correct: C

Using the disk method, the volume V is given by the integral of π[f(x)]^2 dx from a to b. In this case, f(x) = x^2, a = 0, and b = 2. So, V = integral from 0 to 2 of π(x^2)^2 dx = π integral from 0 to 2 of x^4 dx = π[x^5/5] from 0 to 2 = π(2^5/5 - 0^5/5) = π(32/5) = 32π/5.