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प्रश्न
A heap of rice in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of rice. How much canvas cloth is required to cover the heap ?
उत्तर
The heap of rice is in the form of a cone.
Diameter, d = 9 m
radius, r = \[\frac{9}{2}m\]
height, h = 3.5 m
\[\text { Volume }, V = \frac{1}{3} \pi r^2 h\]
\[ = \frac{1}{3}\pi \left( \frac{9}{2} \right)^2 \times 3 . 5\]
\[ = 74 . 25 m^3\]
Thus, volume of rice = 74.25 m3
The canvas cloth required to cover the heap will be the curved surface area of the cone
\[l = \sqrt{h^2 + r^2}\]
\[l = \sqrt{3 . 5^2 + \left( \frac{9}{2} \right)^2}\]
\[l = \sqrt{12 . 25 + 20 . 25}\]
\[l = 5 . 7 m\]
\[CSA = \pi rl\]
\[ = \pi \times \left( \frac{9}{2} \right) \times 5 . 7\]
\[ = 80 . 62 m^2\]
Hence, the canvas cloth required to cover the heap will be 80.62 m2
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