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# The radii of circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and volume of frustum.

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In this question we have to find the total surface
area and volume of frustum given that the radii of
circular bases of a frustum of a right circular cone
are 12 cm and 3 cm and the height is 12 cm.

This question is from r d sharma class 10 maths.
I found this question while doing mensuration of
class 10.
I need help in getting the solution.

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1. Given the height of frustum cone = 12 cm

Radii of a frustum cone are 12 cm and 3 cm

So, r1 = 12 cm; r2 = 3 cm

Let slant height of the frustum cone be ‘L’

Then, we know that

L = 15 cm

Now, the total surface area of frustum of a cone = π (r1 + r2) x L + π r12 + π r22

= π (12 + 3)15 + π122 + π32

Thus, total surface area of the frustum = 378 π cm2

Next,

Volume of frustum cone = 1/3 π(r22 + r12 + r1 r2 )h

= 1/3 π(122 + 32 + 12 × 3) × 12 = 756π cm3

Therefore, the volume of the frustum cone = 756 π cm3

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