In the given problem given shape is hemisphere. To find answer of this question need to use hemisphere volume formula. Given problem from RS Aggarwal book page number 810, problem number 13, chapter volume and surface area of solid, exercise 17B,Chapter Mensuration

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# 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

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Radius of hemisphere = 9 cm

Volume of hemisphere = [2/3] πr³

=[2/3] π 9³

Height of cone = 72 cm …….given

the radius of the cone be r

Volume of the cone = [1/3] πr²h

= [1/3] π * r² * 72

now,

volumes of the hemisphere = volume of the cone

[2/3] π 9³ = [1/3] π * r² * 72

r² = [2 * 9³] / 72

r² = 81/4

r = √[81/4]

r = 9/2

r = 4. 5 cm

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