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 approximate error in calculating its volume?

(a) 16 cu cm

(b) 15 cu cm

(c) 15.5 cu cm

(d) 14 cu cm

I have been asked this question in unit test.

I'm obligated to ask this question of Application of Derivative for Error Determination topic in section Application of Derivatives of Mathematics – Class 12

Answer 1

The correct choice is (b) 15 cu cm

The explanation: 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 cu cm.