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 10 m and diameter 14 m. The
remaining cloth was used for the floor.
10 m
i How much Cloth was used for the floor?
a. 31.6 m2
b. 16 m2
C. 10 m2
d. 20 m²
ii. What was the volume of the tent?
Answers
Given : 300 sq.m cloth used to make tent ,.
conical tent with height 10m and diameter 14m.
The remaining cloth was used for the floor
To find :
i) How much cloth was used for the floor?
a. 31.6 m2
b. 16 m2
C. 10 m2
d. 20 m²
ii) What was the volume of the tent?
Solution:
conical tent with height 10m and diameter 14m.
=> radius = 14/2 = 7 m
h = 10 m
slant height L = √7² + 10² = √149 m
slant height of the tent = 10 m
Lateral surface Area = πRL
= π ( 7) √149
= 268.4 m²
cloth used for the floor = 300 - 268.4 = 31.6 m²
volume of the tent = (1/3)πR²h
= (1/3)(22/7)*7²*10
=513.33 m³
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Given :
- cloth used to make tent = 300 m².
- Height of conical tent = 10m and
- Diameter of conical tent = 14m.
- The remaining cloth was used for the floor .
To find :
(i) How much cloth was used for the floor ?
(a) 31.6m² (b)16m² (c) 10m² (d)20m²
(ii) What was the volume of the tent ?
(a)300m³ (b)160m³ (c)513.3m³ (d)500m³
(iii)What was the area of the floor ?
(a)50m² (b)100m² (c)150m² (d)154m²
(iv)What was the T.S.A of the tent ?
(a)400m² (b)422.4m² (c)300m² (d)400m²
(v) What was the slant height of the tent ?
(a)12m (b)12.2 m (c)15 m (d)17 m
Solution :-
we know that,
- Radius = (Diameter/2) .
- Slant height = [Radius² + Height²]
- CSA of cone = π * radius * slant height .
- Base area of cone = π * (radius)² .
- TSA of cone = CSA + Base Area.
- Volume of cone = (1/3) * π * (radius)² * height .
Answer (iii) :-
→ Area of the floor = (14/2) = 7 m.
→ Cloth used for floor = Base Area of conical tent = π * (radius)² = (22/7) * 7 * 7 = 154 m² (d) (Ans.)
Answer (v) :-
→ Slant height of tent = √(r² + h²) = √(7² + 10²) = √(49 + 100) = √(149) ≈ 12.2 m (b) (Ans.)
Answer (i) :-
→ cloth was used for the floor = Total cloth - CSA of conical tent = 300 - {(22/7) * 7 * 12.2} = 300 - 268.4 = 31.6 m² (a) (Ans.)
Answer (iv) :-
→ T.S.A of the tent = CSA + Base Area = 268.4 + 154 = 422.4 m². (b) (Ans.)
Answer (ii) :-
→ Volume of the tent = (1/3) * (22/7) * (7 * 7) * 10 = (1540/3) ≈ 513.3 m³ (c) (Ans.)
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