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If the radii of the circular ends of a frustum of height $6 cm$ are $15 cm$ and $7 cm$ respectively, then what is the volume and lateral surface area (curved surface area) of the frustum [take $π = 3.14]$ ?

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2382 cm 3

690 cm 2

2382.2 cm 3

690.8 cm 2

2002.2 cm 3

670.7 cm 2

2364 cm 3

580 cm 2

answer is B.

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Detailed Solution

Given that the radii of the circular ends of a frustum of height

6 cm

are

15 cm

and

7 cm

.
We have the following formulae,
CSA of frustum

= π (R + r) l

Slant height

l = h 2 + (R − r) 2

Volume of frustum

= 13 π h R 2 + r 2 + R r

The volume of the frustum will be,

= 13 × 227 × 6 72 + 152 + 15 × 7

= 6.2857 (379) = 2382.2 cm 3

l = 62 + (8) 2 = 36 + 64 = 10 cm

CSA of frustum will be,

= 227 × (22) × 10 = 690.8 cm 2

Thus, the volume is

2382.2 cm 3

and the curved surface area of frustum is

690.8 cm 2

.
Therefore the correct option is 2.

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