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# A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm and height 3 cm. Find the area of its whole surface and volume.

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I would like to give a question which
i could not solve.
Rd sharma class 10 maths exercise-16.3 mensuration.

In this question we have to find the area
of its whole surface and volume given that
a frustum of a right circular cone has a diameter
of base 20 cm, of top 12 cm and height 3 cm.

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1. Given,

Base diameter of cone (d1) = 20 cm

So the radius (r1) = 20/2 cm = 10 cm

Top diameter of Cone (d2) = 12 cm

So, the radius (r2) = 12/2 cm = 6 cm

Height of the cone (h) = 3 cm

Volume of the frustum of a right circular cone = 1/3 Ï€(r22 + r12 + r1 r2 )h

= Ï€/3(102 + 62 + 10 Ã— 6)3

= 616 cm3

Let â€˜Lâ€™ be the slant height of cone, then we know that

L = âˆš(r1 â€“ r21)2 + h2

L = âˆš(10 â€“ 6)2 + 32

L = âˆš(16 + 9)

L = 5cm

So, the slant height of cone (L) = 5 cm

Thus,

Total surface area of the frustum = Ï€(r1 + r2) x L + Ï€ r12 + Ï€ r22

= Ï€(10 + 6) Ã— 5 + Ï€ Ã— 102 + Ï€ Ã— 62

= Ï€(80 + 100 + 36)

= Ï€(216)

= 678.85 cm2

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