Question

A metallic cone having base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is

(a) 2.1 cm (b) 1.05 cm (c) 1.5 cm (d) 2 cm

Answer 1

For the cone,
radius, r = 2.1cm
height, h = 8.4 cm

For the sphere,
radius = R

Cone is melted and recast into sphere.
So, Volume of sphere = Volume of cone
∴ π R³ = π r² h
∴4 R³ = r² h
∴4 R³ = 2.1² $\times$ 8.4
∴R³ = 2.1²$\times$
∴R³ = 2.1²$\times$ 2.1
∴R³ = 2.1³
∴R = 2.1 cm