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Surface Areas and Volumes
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31/07/2021 10:47 am
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A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas.
(Assume π = 22/7)
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31/07/2021 10:51 am
Radius (r) of heap = \(\frac{10.5}{2}\) m
= 5.25
Height (h) of heap = 3m
Volume of heap = \(\frac{1}{3}\)πr2h
= \(\frac{1}{3}\) × \(\frac{22}{7}\) × 5.25 × 5.25 × 3
= 86.625
The volume of the heap of wheat is 86.625 m3.
Area of canvas required = CSA of cone = πrl,
where l = \(\sqrt{r^2 + h^2}\)
After substituting the values, we have
CSA of cone = [\(\frac{22}{7}\)x 5.25 x \(\sqrt{(5.25)^2 + 3^2}\)]
= \(\frac{22}{7}\) × 5.25 × 6.05
= 99.825
Therefore, the area of the canvas is 99.825 m2.