Question

Error in the measurement of radius of a sphere is 1%. Then error in the measurement of volume is
(A) 1% (B) 5%(C) 3% (D) 8%

Answer 1

Answer:

here is your answer thank you

Answer 2

Answer:-

3%

Explanation:

In this Question,

We have been given that,

Error in the measurement of the sphere is 1%

We need to find the error in the measurement of volume.

According to the Question

We know that Volume of the Sphere is given by = $\frac{4}{3}\times \pi\times r^{3}$

Differentiating with respect to r we get,

$\frac{\mathrm{d} v}{\mathrm{d} r}\ =\ \frac{4}{3}\times 3r^{2}$

dv = $4r^{2}$dr

Error in volume = $\frac{\Delta{v}}{v}\times 100$

Error in Volume = $\frac{4r^{2}dr}{\frac{4}{3}\times \pi\times r^{3}}\times 100$

Error in Volume = $\frac{3dr}{r}$

$\frac{dr}{r}\ =\ 1\%$

Error in Volume = 3×1%

Error in Volume = 3%