Allied & ICAR Exam Bank • ALLIED_2688 NAT • 2 Marks

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Physical interpretations – line, surface and volume integrals

Question Statement:

The value of $\iint_S dS$ over the surface of a sphere of radius $R = 2$ is $k \pi$. The integer $k$ is:

Answer Key:

16

Step-by-Step Solution & Explanation

The surface integral $\iint_S dS$ gives the total surface area of the sphere: $A = 4\pi R^2 = 4\pi(2^2) = 16\pi$. Thus $k = 16$.
← Previous (ALLIED_2687) Next (ALLIED_2689) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test