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

= `22/7 xx 14 xx 14`

= 22 × 7 × 14

Area = 616 m²

(iii)

(a) Area of cloth used for making tent. 

= 2πrh × πlr = 2πr [h + l]

= `2 xx 22/7 xx 14 [8 + 17.5]`

= 2 × 22 × 2 [25.5]

= 88 × 25.5 = 2244 m² 

            OR

(b) Total volume Inside the Test  

= `pir^2h + 1/3pir^2h = pir^2(h + 1/(3h))`

= `22/7 xx 14 xx 14 (8 + 1/3 xx 10.5)`

= 22 × 2 × 14 (8 + 3.5)

= 616 × 11.5 = 7084 cm³