Pages

Once four friends Rahul, Arun, Ajay and Vijay went for a picnic . . .

Case Study based Question 

Read the Source / Text given below and answer all four questions:

Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due to peak season they did not get a proper hotel in the city. The weather was fine so they decided to make a conical tent at a park. They were carrying 300 m² cloth with them. As shown in the figure they made the tent with height 10m and diameter 14 m. The remaining cloth was used for the floor. [4 Marks].


Doubt by Saksham

i. Slant height of the tent is 
a) 12 m
b) 12.2 m 
c) 15 m
d) 17 m 

ii. Area of the cloth used for the floor is 
a) 31.6 m²
b) 16 m²
c) 10 m²
d) 20 m²

iii. Volume of the tent is 
a) 300 m³
b) 160 m³
c) 513.3 m³
d) 500 m³

iv. The area of the floor is 
a) 50 m²
b) 100 m²
c) 150 m²
d) 154 m²

Solution : 

height (h) = 10m
diameter (d) = 14 m
radius (r) = 14/2 = 7 m
Total area of the cloth = 300 m²

i. l=√(h²+r²)
l=√[(10)²+(7)²]
l=√[100+49]
l=√149
l=12.2 m
Hence, b) would be the correct option. 

ii. Area of cloth used for the floor
= Total Area of cloth - Area of cloth used in Tent
= Total Area of cloth - CSA of Conical Tent  
= 300 - πrl
= 300 - (22/7)×7×12.2
= 300-(22×12.2)
= 300-268.4
= 31.6 m²
Hence, a) would be the correct option. 

iii. Volume of the Tent
= Volume of the cone
= (⅓)πr²h
=(⅓)×(22/7)×(7)²×10
= (⅓)×22×7×10
= (⅓)×1540
= 513.33 m³
Hence, c) would be the correct option.

iv. Area of the floor of the tent
= Area of the circular base of the conical tent
= πr²
= (22/7)×7×7
= 154 cm²
Hence, d) would be the correct option.