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The slant height of a frustum of a cone is 3 cm and the perimeters of its circular ends are 20 cm and 16 cm. Find the curved surface area of the frustum.
1. 32 cm2
2. 54 cm2
3. 42 cm2
4. 33 cm2

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Correct Answer - Option 2 : 54 cm2

Given:

Perimeter of upper circular end of frustum = 20 cm

Perimeter of lower circular end of frustum = 16 cm

Slant height (l) of frustum = 3 cm

Formula used:

Curved surface area of frustum = π(r1 + r2)l

Where, r1 = Radius of upper base of frustum

r2 = Radius of lower base of frustum

Perimeter of circle = 2

πr

Calculation:

Perimeter of upper circular end of frustum = 20 cm

⇒ 2πr1 = 20

⇒ r1 = 10/π 

Again,

Perimeter of lower circular end of frustum = 16 cm

⇒ 2πr2 = 16

⇒ r2 = 8/π 

According to the question:

Curved surface area of frustum = π(r1 + r2)l

⇒ 3π (10/π + 8/π)

⇒ 3 × (18/π) × π 

⇒ 3 × 18 = 54

∴ The curved surface area of the frustum is 54 cm2.

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