Question

If the radius of a sphere is measured as 6 m with an error of 0.02 m, then find the approximate error in calculating its surface area.

• A. (A) 0.48 square meters
• B. (B) 0.96 square meters
• C. (C) 1.20 square meters
• D. (D) 0.72 square meters

Answer 1

Answer: (B)

(B) 0.96 square meters

Answer 2

Explanation:
Let, the radius of a sphere is r meters.The surface area of Sphere (A)=4πr2Given: Radius of a sphere =6m and Δr=0.02mNow, the volume of the sphere is given by,A=4πr2Differentiating with respect to r, we get:dSdr=8πr⇒dS=8mr⋅dr⇒dS=8π⋅6⋅(0.02)⇒dS=0.96 square metersHence, the correct option is (B).