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# A rent cylindrical to a height to 4.8 m and conical above it. The radius of the base is 4.5 m. And the total height of the tent is 10.8 m. Find the canvas required for the tent in square meters.

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Hint: This is a popular problem of mensuration. First we have to compute the total curved surface area of the tent, which will be the combination of a cone and a cylinder. Then we can find the canvas for a tent in square meters.

Complete step-by-step answer:

Given data in the problem are:
Total height tent (H) = 10.8 m
Height of cylinder (h) =4.8 m
Height of cone = (10.8 - 4.8) = 6 m
Radius of cylinder and cone (r) = 4.5 m
For the cone slant height is needed to get its surface area.
And slant height =
l = $\sqrt {{{4.5}^2} + {6^2}} \\ \Rightarrow \sqrt {56.25} \\ \Rightarrow 7.5m \\$
Curved surface area of cone = $\pi rl$
Curved surface area of cylinder =$2\pi rh$
Now, total canvas required = curved surface area of cone +curved surface area of the cylinder
$\Rightarrow \pi rl + 2\pi rh \\ \Rightarrow \pi r(l + 2h) \\ \Rightarrow \dfrac{{22}}{7} \times 4.5 \times (7.5 + 2 \times 4.8) \\ \Rightarrow \dfrac{{22 \times 4.5 \times 17.1}}{7} \\ \Rightarrow 241.85{m^2} \\$

The total area of canvas required will be 241.85 square meters.

Note: In mensuration, proper understanding of the shape of the object is very important to get the correct solution. Also, proper implementation of the related formulas in proper units is very essential too. Therefore all related formulas must be known for the correct answer of the problems.