The volume of a cube is increasing at the rate of 9 cm3/s. The rate at which the length of its edge is increasing when the edge is 10 cm long is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.03 cm/s
Let x be the edge and V the volume at time t. Then
\(V = x^3\)
Differentiating with respect to t by the chain rule:
\( \displaystyle \frac{dV}{dt} = 3x^2\,\frac{dx}{dt} \)
\( \displaystyle 9 = 3 \times 100 \times \frac{dx}{dt} \)
\( \displaystyle \frac{dx}{dt} = \frac{9}{300} = 0.03 \) cm/s