Question

A hemisphere of lead of radius 7/2 cm is cast into a right circular cone of height 49/2cm. Find the base radius of the cone.

Answer 1

Step-by-step explanation:

Given,

Radius of hemispher R=7 cm

Hight of cone h=49 cm

Volume of hemisphere V= 2/3 πR ^3

= 2/3 π×(7)^3 cm ^3

=2/3 ×343×π cm ^3 =686/3 π cm ^3

Volume of cone V= 1/3 πr ^2 h = 1/3 πr ^2×49 cm

The hamisphere is cast into a right circular cone of hight (h=49 cm) and have base radius r.

→Volume of hemisphere = Volume of cone

686/3 π cm ^3 = 49/3 πr ^2 cm

r ^2 =686/49 cm ^2

r ^2=14 cm ^2

r= 14cm

Hence, radius of base of cone r=3.74 cm