A copper sphere of radius 3 cm is melted and recast into a right circu

1.	A copper sphere of radius 3 cm is melted and recast into a right circular cone of height 3 cm. Find the radius of the base of the cone?
Answer» Given, Radius of the copper sphere = 3 cm We know that, Volume of the sphere = 4/3 π r³ = 4/3 π × 3³ ….. (i) Also, given that the copper sphere is melted and recasted into a right circular cone Height of the cone = 3 cm We know that, Volume of the right circular cone = 1/3 π r²h = 1/3 π × r²× 3 ….. (ii) On comparing equation (i) and (ii) we have, 4/3 π × 3³ = 1/3 π × r²× 3 r² = 36 r = 6 cm Therefore, the radius of the base of the cone is 6 cm.

A copper sphere of radius 3 cm is melted and recast into a right circular cone of height 3 cm. Find the radius of the base of the cone?

Answer»

Given,

Radius of the copper sphere = 3 cm

We know that,

Volume of the sphere = 4/3 π r³

= 4/3 π × 3³ ….. (i)

Also, given that the copper sphere is melted and recasted into a right circular cone

Height of the cone = 3 cm

We know that,

Volume of the right circular cone = 1/3 π r²h

= 1/3 π × r²× 3 ….. (ii)

On comparing equation (i) and (ii) we have,

4/3 π × 3³ = 1/3 π × r²× 3

r² = 36

r = 6 cm

Therefore, the radius of the base of the cone is 6 cm.