Question

An edge of a variable cube is increasing at the rate of 10 cm/sec. How fast the volume of the cube will increase when the edge is 5 cm long

• A. 750 ${cm}^3/sec$
• B. 75 ${cm}^3/sec$
• C. 300 ${cm}^3/sec$
• D. 150 ${cm}^3/sec$

Answer 1

The correct option is A 750 ${cm}^3/sec$

If is the length of each side of the cube and $V$is the volume, then

$\begin{array}{c}\frac{ds}{dt}=10\\ V=\frac{s^{3}dv}{dt}=\frac{3\times s^{3}ds}{dt}\\ Ats=5cm,\\ \frac{dv}{dt}=\frac{3\times 5^2\times 10c{m}^3}{s}\\ =750c{m}^3/s\end{array}$