If a cone and a hemisphere have equal radii and heights then the ratio

1.	If a cone and a hemisphere have equal radii and heights then the ratio of its volumes is …………A) 1 : 2 B) 3 : 1 C) 4 : 1 D) 1 : 1
Answer» Correct option is: A) 1 : 2 Height of hemisphere = Radius of hemisphere = r. \(\because\) Heights of cone and hemisphere are equal. \(\therefore\) Height of cone = r = Radius of base of cone. \(\therefore\) \(\frac {V_1}{V_2} \) = \(\frac {Volume \,of \,cone}{Volume \, of\, hemisphere} = \frac {\frac 13 \pi r^2 h}{\frac 23 \pi r^3}\) = \(\frac h{2r} = \frac r {2r} = \frac 12 \) (\(\because\) h = r) = 1 : 2 Hence the ratio of their volumes is 1 : 2 Correct option is: A) 1 : 2

If a cone and a hemisphere have equal radii and heights then the ratio of its volumes is …………A) 1 : 2 B) 3 : 1 C) 4 : 1 D) 1 : 1

Answer»

Correct option is: A) 1 : 2

Height of hemisphere = Radius of hemisphere = r.

\(\because\) Heights of cone and hemisphere are equal.

\(\therefore\) Height of cone = r = Radius of base of cone.

\(\therefore\) \(\frac {V_1}{V_2} \) = \(\frac {Volume \,of \,cone}{Volume \, of\, hemisphere} = \frac {\frac 13 \pi r^2 h}{\frac 23 \pi r^3}\)

= \(\frac h{2r} = \frac r {2r} = \frac 12 \) (\(\because\) h = r)

= 1 : 2

Hence the ratio of their volumes is 1 : 2

Correct option is: A) 1 : 2