Question

The slant height of a frustum of a cone is 4 cm and the perimeters (circumferences) of its circular ends are18 cm and 6 cmthen the curved surface area of the frustum is _______. 1

Answer 1

2pie×R =18
pie×R=9
2 pie×r=6
pie×r= 3
circumference of frustum
=pie×R×l+pie×r×l
=9×4+3×4
=48 cm (square)

Answer 2

Given,

Slant height of frustum of cone (l) = 4 cm

Let ratio of the top and bottom circles be r1 and r2

And given perimeters of its circular ends as 18 cm and 6 cm

⟹ 2πr1 = 18 cm; 2πr2 = 6 cm

⟹ πr1= 9 cm and πr2 = 3 cm

We know that,

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

= (πr1+πr2)l = (9 + 3) × 4

 = (12) × 4 = 48 cm2

Therefore, the curved surface area of the frustum = 48 cm2.