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
Answers
Given : 200 sq.m cloth used to make tent ,.
conical tent with height 8m and diameter 12m.
The remaining cloth was used for the floor
To find :
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?
Solution:
conical tent with height 8m and diameter 12m.
=> radius = 12/2 = 6 m
h = 8 m
slant height L = √6² + 8² = 10 m
slant height of the tent = 10 m
Lateral surface Area = πRL
= π ( 6) ( 10)
= 60π
= 60 x 3.14
= 188.4 m²
cloth used for the floor = 200 - 188.4 = 11.6 m²
volume of the tent = (1/3)πR²h
= (1/3)(3.14)*6²*8
= 301.44 m³
area of the floor = πR²
= 3.14 (6)²
= 113.04 m²
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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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