Q. An edge of a variable cube is increasing at the rate of 10cm/s. How fast the volume of the cube will increase when the edge is 5 cm long?
A) 750 cm $\frac{3}{s}$
B) 75 cm $\frac{3}{s}$
C) 300 cm$\frac{3}{s}$
D) 150 $cm\frac{3}{s}$
Explanation
(a)
Let $l$be the length of an edge and $V$be the volume of cue at any time $t.$
$\because\ \ \ \ V = t^{3}$
$\because\ \ \frac{dV}{dt} = 3l^{2}\frac{dl}{dt}$
$\ \ \ \ = 3 \times 5^{2} \times 10cm^{3}/s$
$\ \ \ \ = 750cm^{3}/s.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.