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प्रश्न
A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap?
उत्तर
Given that a heap of rice is in the form of a cone.
Height of a heap of rice (h) = 3.5 m
And diameter of a heap of rice = 9 m
∴ Radius of a heap of rice (r) = `9/2` m ...`[∵ "Radius" = 1/2 xx "diameter"]`
So, volume of rice = `1/3π"r"^2"h"`
= `1/3 xx 22/7 xx 9/2 xx 9/2 xx 3.5`
= `6237/84`
= 74.25 m3
Now, canvas cloth required to just cover heap of rice
= Surface area of a heap of rice
= πrl
= `22/7 xx "r" xx sqrt("r"^2 + "h"^2)`
= `22/7 xx 9/2 xx sqrt((9/2)^2 + (3.5)^2)`
= `(11 xx 9)/7 xx sqrt(81/4 + 12.25)`
= `99/7 xx sqrt(130/4)`
= `99/7 xx sqrt(32.5)`
= 14.142 × 5.7
= 80.61 m2
Hence, 80.61 m2 canvas cloth is required to just cover the heap.
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