Question

The error in the measurement of radius of a sphere is 2%. What would be the error in : ( A = 4π R^2)
A) 4 %
B) 3 %
C) 2 %
D) 1 %

Answer 1

Need to FinD :-

• The error in the measurement of surface area .

$\red{\frak{ Given }}\Bigg\{ \textsf{ The error in the measurement of radius of a sphere is 2 \% . }$

The error in the measurement of the radius is 2% . We know the surface area of sphere as ,

$\sf\longrightarrow Surface\ Area = 4\pi r^2$

Since the percentage error in measurement of Radius is 2% . Therefore ,

$\sf\longrightarrow\dfrac{\Delta r }{r}= 2\%$

Therefore, the percentage error in measurement of surface area will be ,

$\sf\longrightarrow \dfrac{\Delta A}{A}\times 100 = \bigg( \dfrac{2\Delta r}{r}\bigg) \times 100 \\\\\\\sf\longrightarrow \dfrac{\Delta A}{A}\times 100 = \dfrac{ 2\times 2 }{100}\times 100 \\\\\\\sf\longrightarrow \underset{\blue{\sf Option \ A }}{\underbrace{\boxed{\pink{\frak{ \dfrac{\Delta A}{A}\times 100 = 4\% }}}}}$

Answer 2

Answer:

The error in the measurement of radius of a sphere is 2%. What would be the error in : ( A = 4π R^2)

A) 4 %

B) 3 %

C) 2 %

D) 1 %

The error in the measurement of radius of a sphere is 2%. What would be the error in : ( A = 4π R^2)

A) 4 %

B) 3 %

C) 2 %

D) 1 %

Explanation:

Option a is correct