Question

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

• A. $750c{m}^3/s$
• B. $75c{m}^3/s$
• C. $150c{m}^3/s$
• D. $25c{m}^3/s$

Answer 1

The correct option is A

$750c{m}^3/s$

Explanation for the correct option:

Calculate the increased volume of the cube : (when the edge is $5$cm long)

Let the edge of the cube be “$x$” cm and edge of a variable cube is increasing at the rate of $10$ cm/s.

$\therefore \frac{dx}{dt}=10cm/s$

$\begin{array}{rcl}VolumeV& =& x^3\\ & & differentiatewithrespectto"t"\\ \frac{dv}{dt}& =& 3x^2\left(\frac{dx}{dt}\right)\\ {\left(\frac{dv}{dt}\right)}_{x=5cm}& =& 3{\left(5\right)}^2\times 10\\ & =& 750c{m}^3/sec\end{array}$

Hence, the correct option is A.