Question

A Cone is 8.4 cm high and the radius of its base is 2.1cm. It is melted and recast into a sphere. Find the radius of sphere formed? Please answer the question in 24 hours(solved).

Answer 1

radius of cone = 1/3πr²h
                         = 1/3 × 22/7 × 2.1 × 2.1 × 8.4
                         = 38.808 cm³
volume of sphere = volume of cone
4/3πr³ = 38.808
r³ = 9.261
r = 2.1 cm

Answer 2

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
∴ 4/3 π R³ = 1/3 π r² h
∴4 R³ = r² h
∴4 R³ = 2.1² * 8.4
∴R³ = 2.1² * 8.4 / 4
∴R³ =  2.1² * 2.1
∴R³ = 2.1³
∴R = 2.1 cm

Thus, radius of the sphere is 2.1 cm.