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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 â€˜Lâ€™

Then, we know that

L = 15 cm

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

= Ï€ (12 + 3)15 + Ï€122 + Ï€32

Thus, total surface area of the frustum = 378 Ï€ cm2

Next,

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

= 1/3 Ï€(122 + 32 + 12 Ã— 3) Ã— 12 = 756Ï€ cm3

Therefore, the volume of the frustum cone = 756 Ï€ cm3

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