Question

An edge of a variable cube is increasing at the rate of 3 cm per second. How fast is the volume of the cube increasing when the edge is 10 cm long?

Answer 1

$$\text{ Let x be the side and V be the volume of the cube at any time t. Then },$$
$$V=x^3$$
$$\Rightarrow \frac{dV}{dt}=3x^2\frac{dx}{dt}$$
$$\Rightarrow \frac{dV}{dt}=3\times {\left(10\right)}^2\times 3[\because x=10cm\text{ and }\frac{dx}{dt}=3cm/sec]$$
$$\Rightarrow \frac{dV}{dt}=900{cm}^3/\sec$$