Question

A solid metallic right circular cylinder of base diameter 16 cm and height 2 cm is melted and recast into a right circular cone of height three-times that of the cylinder. The curved surface area of the cone will be: (Use π - 3.14)
1. 254.8 cm²
2. 251.2 cm²
3. 250.4 cm²
4. 248.6 cm²

Answer 1

Correct Answer - Option 2 : 251.2 cm²

Given:

Right circular cylinder of height 2 cm and base diameter 16 cm recast into right circular cone of height 3 times

π = 3.14

Concept:

When anything is recast volume remains same

Volume of cone is equal to volume of cylinder

Formula:

Volume of right circular cylinder = πr²h

Volume of right circular cone = 1/3πr²h

Where r is radius, h is height

Radius = 1/2 × base diameter

L² = h² + r²

Where L is slant height, h is height and r is radius.

Curved surface area = πrL

Calculation:

Height of right circular cone = 3 × 2 = 6 cm

Let radius of right circular cone be r

Radius of right circular cylinder = 1/2 × 16 = 8 cm

Volume of right circular cylinder = π × 8² × 2 = 128π cm³

Volume of right circular cone = 1/3 × π × r² × 6 = 2πr² cm³

2πr² = 128π

⇒ 2r² = 128

⇒ r² = 64

⇒ r = 8

Let slant height be l

l² = 6² + 8² = 100 cm²

⇒ l = 10 cm

Curved surface area = (3.14 × 8 × 10) cm² = 251.2 cm²

∴ Curved surface area of the right circular cone is 251.2 cm²