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Question
The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its volume \[\pi\] = 3.14)
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Solution
Here, r1 = 14 cm, r2 = 6 cm and h = 6 cm.
Slant height of the frustum, l = \[\sqrt{h^2 + \left( r_2 - r_1 \right)^2} = \sqrt{6^2 + \left( 14 - 6 \right)^2} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100}\]= 10 cm
Volume of the frustum
\[= \frac{1}{3}\pi h\left( r_1^2 + r_1 r_2 + r_2^2 \right)\]
\[ = \frac{1}{3} \times 3 . 14 \times 6 \times \left( {14}^2 + 14 \times 6 + 6^2 \right)\]
\[ = 3 . 14 \times 2 \times \left( 196 + 84 + 36 \right)\]
\[ = 6 . 28 \times 316\]
\[ = 1984 . 48 {cm}^3\]
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