Question

Find the surface area of frustum in cm², If perimeter of its circular ends are 88 cm and 22 cm. and slant height is 30 cm.
1. 1336.5 cm²
2. 1888 cm²
3. 1650 cm²
4. 2250 cm²

Answer 1

Correct Answer - Option 3 : 1650 cm²

Given:

Perimeter of bigger circular end = 88 cm

Perimeter of smaller circular end = 22 cm

Slant height = 30 cm

Formula used:

Perimeter of circular part = 2πr

Surface area of frustum = π(R + r) × L

Where, L → slant height, R → radius of bigger end, r → radius of smaller end

Calculation:

Perimeter = 2πR

⇒ 88 = 2π × R

⇒ R = 88/2π = (44 × 7)/22

⇒ R = 14 cm

Perimeter = 2πr

⇒ 22 = 2π × r

⇒ r = 22/2π 

⇒ r =3.5 cm

Surface area of frustum = π(R + r) × L

⇒ π(14 + 3.5) × 30

⇒ π × 17.5 × 30

⇒ 1650 cm²

∴ The surface area of frustum is 1650 cm2