Question

The radius of a sphere is measured to be $20cm$ with a possible error of $0.02$ of a$cm$. The consequent error in the surface of the sphere is

• A. $10.5sq.cm$
• B. $5.025sq.cm$
• C. $10.05sq.cm$
• D. None of these

Answer 1

The correct option is C

$10.05sq.cm$

Explanation for the correct answer:

Given,

Radius of the sphere is $20cm$, possible error of $0.02$$cm$.

We need to find the consequent error in the surface of the sphere

We know that the surface area of a sphere is,

$S=4\pi r^2$

Where,

$S$ is the surface area of the sphere

$r$ is the radius of the sphere.

On differentiating the above equation with respect to $r$

$\partial S=8\pi r(\partial r)$

$$\begin{gathered} =8\pi \times 20\times 0.02 \\ =10.05sq.cm \end{gathered}$$

Hence the error in the surface of the sphere is $\mathbf{\text{10.05 sq.cm}}$.