# A Hemisphere of Lead of Radius 9 Cm is Cast into a Right Circular Cone of Height 72 Cm. Find the Radius of the Base of the Cone. - Mathematics

Sum

A hemisphere of lead of radius 9 cm is cast into a right circular cone of height 72 cm. Find the radius of the base of the cone.

#### Solution

Radius of hemisphere = 9 cm

Volume of hemisphere = 2/3pir^3= 2/3pixx9xx9xx9   "cm"^3

Height of cone = 72 cm

Let the radius of the cone be r cm.

Volume of the cone = 1/3pir^2h=1/3pir^2xx 72  "cm"^3

The Volume of the hemisphere and cone are equal.

Therefore,

1/3pir^2xx72xx =2/3xx9xx9xx9xx9

r^2 =(2xx9xx9xx9)/72 = 81/4

r = sqrt(81/4) = 9/2 = 4.5  "cm"

The radius of the base of the cone is 4.5 cm.

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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Exercise 19B | Q 13 | Page 898