The word circus has the same root as circle. In a closed circular . . .

Case Study Based Question on Surface Area and Volume

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 8m and conical above it. The diameter of the base is 28 m and total height of the tent is 18.5 m.

Based on the above, answer the following questions : 

(i) Find the slant height of the conical part. (1 Mark)

(ii) Determine the floor area of the tent. (1 Mark)

(iii) (a) Find the area of the cloth used for making tent. 

OR

(b) Find total volume of air inside an empty tent.

CBSE 2024 

Solution : 

Height of cylinder (H) = 8 m
Diameter of the base (d) = 28 m 
Radius of the base (r) = 28/2 = 14 m
Total Height of the tent = 18.5 m
Height of cone (h) = 18.5-8 = 10.5 m

(i) Slant height of the conical part
l=√[r²+h²] 
l=√(14)²+(10.5)²
l=√[196+(21/2)²]
l=√[196+(441/4)]
l=√[784+441]/4
l=√1225/4
l=35/2 m
l=17.5 m

(ii) Floor area of the tent = πr²
= (22/7)×14×14
=44×14
=616 m²

(iii) (a) 
Area of the cloth used for making tent
= CSA of cylinder + CSA of Cone
=2πrH+πrl
=πr[2H+l]
=(22/7)(14)[2(8)+17.5]
=22×2[16+17.5]
=44[33.5]
=1474 m²

OR 

(b) Volume of the air inside the tent
=Volume of the cylinder + Volume of the cone
= πr²H+1/3πr²h
=πr²[H+h/3]
=(22/7)×(14×14)[8+10.5/3]
=22×2×14[8+3.5]
=44×14×11.5
=7084 m²