Question

A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49cm. find the radius of the base?​

Answer 1

Answer:

Radius of the base =3.74cm.

Answer 2

Answer:

Given:-

• Radius of hemisphere R = 7 cm.
• Hight of cone h = 49 cm.

Solution:-

Volume of hemisphere, V = 2/3πr³.

Volume of hemisphere, V = 2/3π × (7)³.

Volume of hemisphere, V = 2/3 × 343 × π.

Volume of hemisphere, V = 686/3π cm³.

Volume of cone, V = 1/3πr²h.

Volume of cone, V = 1/3πr² × 49 cm.

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

→ Volume of hemisphere = Volume of cone.

→ 686/3π = 49/3.

→ r² = 686/49.

→ r² = 14cm.

→ r = √14cm.

→ r = 3.74cm.

Hence, radius of base of cone r = 3.74cm .

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