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Q.

A circus tent is cylindrical to a height of 6m and conical above it. If its diameter is 105 m and slant height of the conical portion is 50 m then the total area of canvas required to build the tent is.(Use $π = 227$ )

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a

10230 m 2

b

14280 m 2

c

14230 m 2

d

12340 m 2

answer is A.

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Detailed Solution

The curved surface of the cylinder is

, where r is the radius of the cylinder and h is the height of the cylinder.
The curved surface of the cone is

, where r is the radius of the base of the cone and L is the pitch of the cone.
We assume that the circus tent is cylindrical up to a height of 6m and above it is conical and its diameter is 105m and the height of the slope of the conical part is 50m.

Radius =

1052 m

We need to find the total canvas area needed to build the tent.
Total required canvas area = curved surface of cylindrical part + curved surface of conical part.
The curved surface area of the cylindrical part is

2 π r h

.

⇒ C . S . A c y l i n d e r = 2 π r h ​ ⇒ r = 1052, h = 6, π = 227 ​ ⇒ → C . S . A c y l i n d e r = 2 × 227 × 1052 × 6 ​ ∴ C . S . A c y l i n d e r = 1980 m 2 ​

Curved surface area of the conical portion is

π r L

.

C . S . A c o n e = π r L ​ ⇒ r = 1052, L = 50 ​ ⇒ → C . S . A c o n e = 227 × 1052 × 50 ​ ∴ C . S . A c o n e = 8250 m 2 ​

Total area =

C . S . A c y l i n d e r + C . S . A c o n e = 1980 + 8250 = 10230 m 2

The correct option is Option 1,

10230 m 2

.

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