Question

A cylinder whose height is 2/3 of its diameter has same volume as that of a sphere of radius 8 cm .The radius of base of the cylinder is

• A. 8 cm
• B. 4 cm
• C. 2 cm
• D. None of these

Answer 1

Answer: (A)

8 cm

Given radius of sphere $r_1=8cm$.
Let the radius of cylinder be $=r$ and height, $h=\frac{2}{3}$ of diameter.
$\Rightarrow$ volume of cylinder$=$ volume sphere
$\Rightarrow \pi r^{2}h=\frac{4}{3}\pi r_1^3$
$\Rightarrow \pi r^2\left(\frac{2}{3}\left(2r\right)\right)=\frac{4}{3}\pi \times 8^3$
$\Rightarrow r^3=8^3$
$\therefore r=8cm$