Question

How many square meters of canvas is required to form a conical tent where height of the tent is 5m and radius of the base is 12m. Also find the cost of the tent if cost per $m^2$ is Rs 100.

Answer 1

Hint: Here the given question need to find the curved surface area of the tent in order to get the total area of the canvas required here, and then it need to find the total cost of the canvas, for which cost of per meter square of canvas is given here.
Formulae Used: Curved surface area of cone:
\[ \Rightarrow A = \pi r\left( {\sqrt {{h^2} + {r^2}} } \right)\]
Where r, is the radius of the base and,
\[ \Rightarrow \sqrt {{h^2} + {r^2}} = l\]
Here “l” is the slant height of the cone.

Complete step-by-step solution:
Here the given question is to first find the surface area of the tent and then find the total cost of the tent, for which cost of per square meter of canvas is given to us, here we know that tent is in the shape of the cone, and to find the surface area of the tent we need to find the surface area of the cone, here on solving we get:
\[
   \Rightarrow A = \pi \times 5\left( {\sqrt {{{12}^2} + {5^2}} } \right) \\
   \Rightarrow A = 3.14 \times 5\left( {\sqrt {144 + 25} } \right) \\
   \Rightarrow A = 15.70\left( {\sqrt {169} } \right) \\
   \Rightarrow A = 15.70\left( {13} \right) \\
   \Rightarrow A = 15.70\left( {13} \right) = 204.1{m^2} \]
Here we get the total surface area of the tent or cone, and the area of the canvas required will be the same as the area of the cone.
Now cost of the canvas can be given by:
\[ \Rightarrow \cos t = 204.1 \times 100 = Rs20410\]

Note: To solve for the statement type question, we always need to first formulate the statement into a mathematical equation and thus solve according to the context given in the question, as for this question we need to use the formulae for the surface area of the cone.