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 200 sq.m cloth with them. They made the conical tent with height 8m and diameter 12m.The remaining cloth was used for the floor
i)What is the slant height of the tent?
ii)How much cloth was used for the floor?
iii)What was the volume of the tent?
iv)What was the area of the floor?
v)What was the total surface area of the tent?
Answers
GIVEN
The area of the cloth = 200 sq. m
The height of the tent = 8m
Diameter of the tent= 12m
TO FIND
i)the slant height of the tent
ii) cloth used for the floor
iii) the volume of the tent
iv) the area of the floor
v)the total surface area of the tent
SOLUTION
radius of a cone = 1/2 × (diameter of the base of the cone)
radius (r) = 6m
slant height = √{(height)² + (radius)²}
= √(8² + 6²)
= √100
=10m (slant height of the cone)
lateral surface area of the cone = π × r × l
= π × 6 × 10
= 60π
cloth used for the tent = 60π
= 60 × 3.14
= 188.4
Total cloth used = cloth used for tent + cloth used for floor
cloth used for floor = total cloth - cloth for tent
= 200 - 188.4
= 11.6 sq. m (area of cloth used for the floor)
volume of a cone =1/3 × πr²h
= 1/3 × π × 6² × 8
= 96π
= 96 × 3.14
= 301.44 cu. m (volume of the tent)
Answer:
v)What was the total surface area of the tent?