Question

Find the approximate error in the volume of the sphere if the radius of the sphere is measured to be 6cm with an error of 0.07cm.

(a) 10.08π cm^3

(b) 10.08cm^3

(c) 10.4πcm^3

(d) 9.08cm^3

This question was posed to me in class test.

Question is taken from Derivatives Application in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

Correct option is (a) 10.08π cm^3

The explanation: Let x be the radius of the sphere.

Then, x=6cm and Δx=0.07cm

The volume of a sphere is given by V=\(\frac{4}{3}\) πx^3

∴\(\frac{dV}{dx}=\frac{4}{3}\) π(3x^2)=4πx^2

dV=(\(\frac{dV}{dx}\))Δx=4πx^2 Δx

dV=4×π×6^2×0.07

dV=10.08π cm^3