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# A Hemisphere of Lead of Radius 6 Cm is Cast into a Right Circular Cone of Height 75 Cm. Find the Radius of the Base of the Cone. - Mathematics

Sum

A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. Find the radius of the base of the cone.

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#### Solution

We have,

Radius of the hemisphere, R = 6 cm and

Height of the cone, h = 75 cm

Let the radius of the base of the cone be r.

Now,

Volume of the cone =Volume of the hemisphere

=> 1/3 pi"r"^2"h" = 2/3pi"R"^3

=> "r"^2 = (2"R"^3)/"h"

=> "r"^2 = 5.76

=>"r"^2 = sqrt(5.76)

∴ r =2.4 cm

So, the radius of the base of the cone is 2.4 cm.

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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Exercise | Q 20 | Page 915
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