Question

What is the volume generated when the region surrounded by y = \(\sqrt{x}\), y = 2 and y = 0 is revolved about y – axis?

(a) 32π cubic units

(b) \(\frac{32}{5} \) cubic units

(c) \(\frac{32π}{5}\) cubic units

(d) \(\frac{5π}{32} \) cubic units

This question was posed to me during an internship interview.

The doubt is from Volume of Solid of Revolution in portion Integral Calculus of Engineering Mathematics

Answer 1

Correct answer is (c) \(\frac{32π}{5}\) cubic units

Best explanation: Limits for y -> 0,2  x = y^2

\(Volume = \int_a^b πx^2 dy\)

\( = \int_0^2 πy^4 dy\)

\( = \Big[\frac{πy^5}{5}\Big]_0^2\)

\( = \frac{32π}{5}\) cubic units.