Question

The edge of a cube is equal to the radius of a sphere. If the edge and the radius increase at the same rate, then the ratio of increase in surface areas of the cube and sphere is

• A. $2\pi :3$
• B. $3:2\pi$
• C. $6:\pi$
• D. none of these

Answer 1

Answer: (B)

$3:2\pi$

Surface area of cube $S_1=6r^2$

$\Rightarrow \frac{d{S}_1}{dt}=12r\frac{dr}{dt}$ .....(i)

Surface area of sphere $S_2=4\pi r^2$

$\Rightarrow \frac{d{S}_2}{dt}=8\pi r\frac{dr}{dt}$ ......(ii)

$\Rightarrow \frac{\frac{d{S}_1}{dt}}{\frac{d{S}_2}{dt}}=\frac{3}{2\pi }$