Question

The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its

i. curved surface area, 

ii. total surface area, 

iii. volume, (π = 3.14)

Answer 1

Given: Radii (r ) = 14 cm, and (r ) = 6 cm, height (h) = 6 cm

Slant height of frustum (l)

i. Curved surface area of frustum 

= πl (r₁ + r₂ ) 

= 3.14 × 10(14 + 6) 

= 3.14 × 10 × 20 = 628 cm²

∴ The curved surface area of the frustum is 628 cm² .

ii. Total surface area of frustum 

= πl (r₁ + r₂ ) + πr₁² + πr₂² 

= 628 + 3.14 × (14)² + 3.14 × (6)² 

= 628 + 3.14 × 196 + 3.14 × 36

= 628 + 3.14(196 + 36) 

= 628 + 3.14 × 232

= 628 + 728.48 

= 1356.48 cm² 

∴ The total surface area of the frustum is 1356.48 cm².

iii. Volume of frustum 

= 1/3 πth(r₁² +r₂² + r₁ × r₂ ) 

= 1/3 × 3.14 × 6(14² + 6² + 14 × 6) 

= 3.14 × 2(196 + 36 + 84) 

= 3.14 × 2 × 316 

= 1984.48 cm³ 

∴ The volume of the frustum is 1984.48 cm³.