A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone

Solution:

Given, a solid metallic hemisphere is melted and recast into a right circular cone.

Hemisphere has radius of 8 cm

Right circular cone has a base radius 6 cm.

We have to find the height of the cone.

Volume of hemisphere = (2/3)πr³

= (2/3)π(8)³

= 1024π/3 cm³

Volume of cone = (1/3)πr²h

= (1/3)π(6)²h

= 12πh cm³

Given, volume of hemisphere = volume of cone

1024π/3 = 12πh

1024/3 = 12h

h = 1024/3(12)

h = 1024/36

h = 28.44 cm

Therefore, the height of the cone is 28.44 cm.

✦ Try This: A solid metallic hemisphere of radius 10 cm is melted and recast into a right circular cone of base radius 4 cm. Determine the height of the cone.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.4 Problem 1

A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone

Summary:

A solid metallic hemisphere of radius 8 cm is melted and recast into a right circular cone of base radius 6 cm. The height of the cone is 28.44 cm

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