Question

A heap of paddy is in the form of a right circular cone whose diameter is 4.2 m and height 2.8m. If the heap is to be covered exactly by a canvas to protect it from rain, the find the area of the canvas needed

Answer 1

Hint:
In this question it is mentioned that the heap of paddy is in a circular cone. Circular cone is the cone in which its height is perpendicular to the radius. Here diameter is 4.2m and radius is half of diameter hence its radius is 2.1 m . If we try to protect paddy from rain then we have to cover its whole curved surface with canvas. The formula for curved surface area is πrl . If we used the canvas below the paddy then extra r2 we need.

Complete step by step solution:
Height is 2.8 m and diameter is 4.2 m
Calculation of slant height, \[l = \sqrt {{r^2} + {h^2}} \]
 \[\begin{array}{l}
 = \sqrt {{{2.1}^2} + {{2.8}^2}} \,\,m\\
 = \sqrt {4.41 + 7.84} \,\,m\\
 = \sqrt {12.25} \,\,m\\
 = 3.5\,\,m
\end{array}\]
Step 1 To cover the heap of paddy completely we need to cover it from all curved sides as well as from top as well as from bottom.
 Lateral surface area of the cone \[ = \pi rl\]
\[\begin{array}{l}
 = \pi \times 2.1 \times 3.5\,\,{m^2}\\
 = 7.35\pi \,\,{m^2}\\
 = 23.079\,\,{m^2}
\end{array}\]
We have calculated lateral surface area and now we proceed to calculate total surface area.
Step 2: Total surface area of cone \[ = \pi rl + \pi {r^2}\]
\[\begin{array}{l}
 = \pi \times 2.1 \times 3.5\,\,{m^2} + \pi \times {2.1^2}\\
 = 7.35\pi + 4.41\pi \,\,{m^2}\\
 = 36.9264\,\,{m^2}
\end{array}\]
Hence the total surface area is 36.9264 ${m^2}$ when we considered that canvas is also used below the paddy.

Note:
Here in this question it is not clear whether canvas is used below the paddy or not. If we use daily life knowledge, we have to find that area also. but some says it is not mention in question so find only lateral area value of taken here for calculation 3.14