Question

A circus tent is cylindrical to a height of 4 m and conical above it. If its diameter is 105 m and the slant height of the cone is 80 m then the total surface area of the canvas required is

Answer 1

Hint: We have to find the total surface area of the tent, for that we will find the area of the two shapes by which the tent is made of. And then finally we find the sum of both the shapes to find the total area of canvas required.

Formula used: Total surface area of the tent is the sum of lateral surface of cone and the lateral surface area of the cylinder \[ = 2\pi rh + \pi rl\]

Complete step-by-step answer:
Here, it is given that for cylinder the diameter = 105 m
We know that radius is nothing but the half of the diameter,
Therefore radius of the cylinder \[ = \dfrac{{105}}{2}\]​m
Also it is given that the height of the cylinder is 4 m
Also for cone it is given that slant height = 80 m and radius\[ = \dfrac{{105}}{2}\]m
Here we have to find the total surface area of the canvas.
That is the total surface area of the canvas is found as the sum of lateral surface of cone and lateral surface area of cylinder
We know that the lateral surface of cone \[ = \pi rl\]
And the lateral surface of cylinder \[ = 2\pi rh\]
Total surface area of the tent\[ = \pi rl + 2\pi rh\]
Let us substitute the value of radius, height and the slant height in the above formula we get,
Total surface area of the tent\[ = \pi \times \dfrac{{105}}{2} \times 80 + 2\pi \times \dfrac{{105}}{2} \times 4\]
Let us substitute the value of \[\pi \] as \[\pi = \dfrac{{22}}{7}\] and solve the above equation we get,
Total surface area of the tent \[ = 13200 + 1320 = 14520{\rm{ }}{m^2}\]
Hence, Total surface area of the canvas required is \[14520{\rm{ }}{m^2}\]

Additional Information: The total surface area of a cone is the sum of the area of its base and the lateral (side) surface. The lateral surface area of a cone is the area of the lateral or side surface only.

Note: Here since the shape of the tent is like one shape kept over the other. To find the total surface area of the tent we should find the area of both the shapes. Also here the radius is the same for both shapes.