Question

The slant height of a frustum of a cone is 10cm and the perimeter of its circular ends are 6cm and 14cm. Find the height of the frustum​

Answer 1

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Here, l = 4 cm

2πr1 = 18 cm

2πr2 = 6 cm

πr1 = 9, πr2 = 3

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

= (πr1 + πr2) × l

= (9 + 3) × 4

= 48 cm2

Answer 2

Let

r and R be the radii of the two circular ends of the frustum of the cone

Then.

2πr=18 and 2πR=28 (Given)

⇒r=

2π

18

and R=

2π

28

⇒r=

π

9

and R=

π

14

∴ The curved surface area of the frustum =π(r+R)l

=π(

π

9

+

π

14

)×10

=23×10=230cm

2

Hence, the curved surface area of the frustum is 230 cm

2