Question

The volume of the solid standing on the area common to the curves \( x^2 = y, y = x \) and cut off by the surface \( z = y - x^2 \) is:

• A. 32
• B. \( \frac{1}{60} \)
• C. \( \frac{1}{32} \)
• D. 48

Hint:

Use triple integrals for calculating volumes in the presence of complex boundaries like curves and surfaces.

Answer 1

The Correct Option is B

Triple integration computes the volume. Establish bounds using the curves and surface, then integrate to find the enclosed volume of the solid.