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Question

Find the approximate change in the volume V of a cube of side $x$ meters caused by increasing side by 1%.

Moderate

A

$0.03 x^{3} m^{3}$
B

$0.05 x^{3} m^{3}$
C

$0.08 x^{3} m^{3}$
D

$0.04 x^{3} m^{3}$

Solution

$The volume of a cube (V) of side x is given by V = x^{3} .$
therefore,
$\begin{aligned} \begin{aligned} d V & = (\frac{d V}{d x}) Δ x \\ = (3 x^{2}) Δ x \\ = (3 x^{2}) (0.01 x) [as 1 % of x is 0.01 x] \\ = 0.03 x^{3} \end{aligned} \\ Hence, the approximate change in the volume of the cube is 0.03 x^{3} m^{3} \end{aligned}$

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