Question

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

Answer 1

The correct answer is $900 cm^3/s$
Let $x$ be the length of a side and $V$ be the volume of the cube. Then,
$V = x^3.$
$\frac{dv}{dt}=3x^2.\frac{dx}{dt} ...$(By chain rule)
It is given that,
$\frac{dx}{dt}=3cm/s dv/dt=3x2(3)=9x2$
Thus, when $x = 10 cm,$
$\frac{dv}{dt}=9(10)^2=900cm^2/s$
Hence, the volume of the cube is increasing at the rate of $900 cm^3/s$ when the edge is $10 cm$ long.