Question

The word ‘circus’ has the same root as ‘circle’. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd. 

A circus tent is cylindrical upto a height of 8 m and conical above it. The diameter of the base is 28 m and total height of tent is 18.5 m.

Based on the above, answer the following questions:

1. Find slant height of the conical part.   [1]
2. Determine the floor area of the tent.     [1]
3. 
   
   1. Find area of the cloth used for making tent.     [2]
                          OR
   2. Find total volume of air inside an empty tent.      [2]

Answer 1

Given:

Cylindrical height = 8 m

Diameter of base = 28 m

Total height of tent = 18.5 m

(i) Radius = 14 m

(Slant height)² = (Height)² + (Radius)²

l² = (10.5)² + (14)²

= 110.25 + 196 

l² = 306.25

l = 17.5 m

(ii) Floor Area of Tent is = πr²

= π × 14²

= 196π

A = 196π m²

(If π = 3.14,
A ≈ 615.44 m²​)

(iii)

(a) Area of cloth used for making tent. 

CSA of cylinder:

2πrh = 2π × 14 × 8

= 224π

CSA of conical part:

πrl = π × 14 × 17.5

= 245π

224π + 245π

= 469π

469π m²

​Using π = 3.14:

469 × 3.14

= 1472 m²

OR

(b) Total volume Inside the Test  

Volume of cylinder:

πr²h

= π × 14² × 8

= 196π × 8

= 1568π

Volume of cone:

`1/3pir^2h = 1/3pi xx 196xx10.5`

`=2058/3pi`

= 686π

Total volume:

1568π + 686π = 2254π

2254π m³

​2254 × 3.14 = 7077.56

7077.56 m³​