The radii of a frustum of a cone are 28 , cm | vedclass

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Question

(A) Given: $R = 28 \, cm$,$r = 7 \, cm$,$h = 72 \, cm$. First,calculate the slant height $l = \sqrt{h^2 + (R - r)^2} = \sqrt{72^2 + (28 - 7)^2} = \sqr

Vedclass · Accepted Answer

$8250 \, cm^2, 10868 \, cm^2, 77616 \, cm^3$

Vedclass · Answer

(A) Given: $R = 28 \, cm$,$r = 7 \, cm$,$h = 72 \, cm$. First,calculate the slant height $l = \sqrt{h^2 + (R - r)^2} = \sqrt{72^2 + (28 - 7)^2} = \sqrt{5184 + 441} = \sqrt{5625} = 75 \, cm$. Curved Surface Area $(CSA)$ $= \pi(R + r)l = \frac{22}{7} 	imes (28 + 7) 	imes 75 = 22 	imes 5 	imes 75 = 8250 \, cm^2$. Total Surface Area $(TSA)$ $= 	ext{CSA} + \pi R^2 + \pi r^2 = 8250 + \frac{22}{7} 	imes (28^2 + 7^2) = 8250 + \frac{22}{7} 	imes (784 + 49) = 8250 + 22 	imes 119 = 8250 + 2618 = 10868 \, cm^2$. Volume $= \frac{1}{3} \pi h (R^2 + r^2 + Rr) = \frac{1}{3} 	imes \frac{22}{7} 	imes 72 	imes (28^2 + 7^2 + 28 	imes 7) = \frac{22 	imes 24}{7} 	imes (784 + 49 + 196) = \frac{528}{7} 	imes 1029 = 528 	imes 147 = 77616 \, cm^3$.

The radii of a frustum of a cone are $28 \, cm$ and $7 \, cm$ and its height is $72 \, cm$. Find its curved surface area,total surface area,and volume.

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