Question

A solid metallic cone of base radius 2.1 cm and height 8.4 cm is melted and recast into a sphere. What is the surface area (in cm²) of the sphere? (use π = 22/7)
1. 55.44
2. 40.65
3. 44.55
4. 36.96

Answer 1

Correct Answer - Option 1 : 55.44

Given:

The radius of the base and height of a metallic solid cone is 2.1 cm and 8.4 cm. It is melted and recast into a sphere.

Means volume of the cone and sphere is same.

Calculation

Volume of the cone = 1/3 π r2 h

= 1/3 π (2.1)2 × 8.4

Let the height of the sphere = R

According to the question,

Volume of the cone = Volume of the sphere

1/3 π r2 h = 4/3 π R³

π (2.1)2 × 8.4 = 4 π R3

(2.1)2 × 8.4 = 4 R3

R3 = (2.1 × 2.1 × 8.4)/4

R³ = 2.1³

R = 2.1 cm

Now; 

Surface Area of Sphere = 4 π R²

= 4 × 22/7 × (2.1)²

= 55.44 cm²

Hence, the surfcae area of sphere is 55.44 cm².