Question

The length of a side of a cube is 10cm; if an error of 0.05cm is made in measuring the side, then what is the value of relative error in calculating its volume?

(a) 0.0016

(b) 0.014

(c) 0.015

(d) 0.0015

This question was posed to me during an online exam.

Query is from Application of Derivative for Error Determination topic in section Application of Derivatives of Mathematics – Class 12

Answer 1

Right choice is (c) 0.015

To explain: Let, v cubic cm be the volume of the cube of the cube of side x cm.

Then, v = x^3

Thus, dv/dx = d/dx(x^3) = 3x^2

Now, dv = dv/dx * δx = 3x^2 * δx

By problem, x = 10 and δx = 0.05

Therefore, approximate error =  dv = 3 * 10^2 * 0.05 = 15 cc cm.

Hence, relative error = dv/v = 15/10^3 = 0.015