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NCERT Exemplar Solutions Class 10 Mathematics Solutions for Surface Areas and Volumes - Exercise 12.4 in Chapter 12 - Surface Areas and Volumes
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A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. How much canvas cloth is required to just cover the heap?
Answer:
According to the question,
Consider conical heap,
Base Diameter = 9 cm
So, base radius, r = 4.5 cm
Height, h = 3.5 cm
We know that,
Slant height,
l=\sqrt{r^{2}+h^{2}} \\ \Rightarrow l=\sqrt{(4.5)^{2}+(3.5)^{2}}=\sqrt{20.25+12.25} \\ \Rightarrow l=\sqrt{32.5}=5.7 \mathrm{~cm}
We also know that,
Canvas requires to just cover heap = Curved surface area of conical heap
And curved surface area of a cone = πrl
Therefore, the canvas required = π(4.5)(5.7) = 80.61 cm2
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