Question

A circus tent is in the shape of a cylinder surmounted by a conical top of same
diameter. If their common diameter is 56 cm, the height of cylindrical part is 6 m and
the total height of the tent above the ground is 27 m, find the area of canvas used in making the tent

Answer 1

Radius = 56/2 = 28 cm = 0.28 m

CSA of Cylinderical part =
$2\pi rh$
=1.056 m(square)

CSA of conical part =
$\pi rl$
21 m(square) (approx.)


Total area of canvas used = 1.056 + 21 m(square)

= 22.056 m(square)

Answer 2

Area of canvas used for making tent =$4132.24\ m^2$

Explanation:

Area of the canvas = Curved surface area  of cone + Curved surface area of cylinder.

Curved surface area  of cone $=\pi r l$ , where r= radius and l= slant height.

Curved surface area of cylinder = $=2\pi r h$ , where r= radius and h= height.

Given : Common diameter =  56 m

Radius = half of diameter = 28 m

Height of cylinder = 6 cm

Curved surface area of cylinder = $=2(3.14) (28) (6)=1055.04\ m^2$  , where $\pi=3.14$

Height of cone : h= 27 m- 6 m      (total height - height of cylinder)

=21 m  

Slant height of cone = $l=\sqrt{r^2+h^2}$

$l=\sqrt{(28)^2+(21)^2}$

$l=\sqrt{784+441}$

$l=\sqrt{1225}=35$

Now , CSA of cone $=\pi r l=(3.14)(28)(35) =3077.2\ m^2$

, where $\pi=3.14$

i.e. The area of canvas used in making the tent =$1055.04+ 3077.2 = 4132.24\ m^2$

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