Question

The radius of the base of the height of a cone are $3cm$ and $5cm$ respectively whereas the radius of the base and height of a cylinder are $2cm$ and $4cm$ respectively. The ratio of the volume of cone to that of the cylinder is :

• A. $1:3$
• B. $15:8$
• C. $15:16$
• D. $45:16$

Answer 1

The correct option is C $15:16$

for cone

$r=3cm$

$h=5cm$

$v_1=\frac{1}{3}\pi r^{2}h$

$v_1=\frac{1}{3}\times \pi \times 9\times 5$

$v_1=15\pi$

for cylinder

$r=2cm$

$h=4cm$

$v_2=\pi r^{2}h$

$v_2=\pi \times 4\times 4$

$v_2=16\pi$

$\frac{v_1}{v_2}=\frac{15\pi }{16\pi }=15:16$