Question

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

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Answer 1

It is given in the question,

Diameter of Cylinder(d)= 56 m
Radius of Cylinder(r) = 56/2 m = 28 m [Hence, Radius is the half of the Diameter].
Height of Cylindrical part = 6m
Now,
C.S.A of Cylinder = 2 x pi x r x h.
=> C.S.A = 2 x 22/7 x 28 x 6
=> C.S.A = 2 x 22 x 4 x 6
=> C.S.A = 1056 m^2

Again,
Cylinder is summounted by Cone.
So,
Radius of Cone = Radius of Cylinder = 28 m
Height of Cone = Total height of tent-Height of Cylinder = (27-6) m = 21 m

Now,
We are required to find out Slant Height of Cone, For which there is a Formula,

=> l^2 = r^2+h^2
=> l^2 = 28x28 + 21x21
=> l^2 = (784+441) m^2
=> l^2 = 1225 m^2
=> l = Root 1225 m^2
=> l = 35 m.

Now,

C.S.A of Cone = pi x r x l
=> C.S.A = 22/7 x 28 x 35
=> C.S.A = 22 x 4 x 35
=> C.S.A = 3080 m^2

Now,

Total Area covered by Canvas = C.S.A of Cylinder + C.S.A of Cone
=> Total area = (1056+3080) m^2
=> Total area = 4136 m^2

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Answer 2

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