Question

An edge of a variable cube is increasing at the rate of 10cm/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

Answer: (A)

$750\,cm^3/sec$

Answer 2

$\frac{dx}{dt}=10. V=x^{3}$ $\Rightarrow \frac{dV}{dt}=3x^{2} \frac{dx}{dt}$ $=3\left(5\right)^{2}\cdot\left(10\right)=750\,cm^{3}\,sec$.