Question

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

Answer 1

Answer:

The radius of a base of a cone is 3.74 cm

Step-by-step explanation:

SOLUTION:

Given :  

Radius of hemisphere, r = 7 cm

Height of a right circular cone ,h = 49 cm

Let, R be radius of a base of a cone

The hemisphere is cast into the right circular cone, Therefore

Volume of hemisphere =  Volume of cone

⅔ πr³ = ⅓ πR²h  

2 r³ = R²h  

2 × 7³ = R² × 49

2 × 49 × 7 = 49R²

R² = (2 × 49 × 7)/49

R² = 14

R = √14  

R = 3.74 cm

Hence, the radius of a base of a cone is 3.74 cm

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

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