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

Answer 1

The Correct Option is B

Explanation:
Let, the radius of a sphere is r meters.The surface area of Sphere $(A)=4\pi r^2$Given: Radius of a sphere $=6m$ and $\mathrm{\Delta }r=0.02m$Now, the volume of the sphere is given by,$A=4\pi r^2$Differentiating with respect to $r$, we get:$\frac{dS}{dr}=8\pi r$$\Rightarrow dS=8mr\cdot dr$$\Rightarrow dS=8\pi \cdot 6\cdot (0.02)$$\Rightarrow dS=0.96$ square metersHence, the correct option is (B).