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 in a park. They were carrying 300 sq metre of cloth with them. They made the tent with the height 10 m and diameter 14 m. The remaining cloth was used for the floor.
1. What was the area of the floor?
2. What was the slant height height of the tent?
3. What was the total surface area of the tent?
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Answers
Step-by-step explanation:
Given 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 in a park. They were carrying 300 sq metre of cloth with them. They made the tent with the height 10 m and diameter 14 m. The remaining cloth was used for the floor.
1. What was the area of the floor?
2. What was the slant height of the tent?
3. What was the total surface area of the tent?
- Given
- Area of the cloth is 300 sq m
- height of the tent is 10 m
- Diameter of the tent is 14 m
- So radius of the conical tent will be ½ x diameter of base of cone
- ½ x 14
- = 7 m
- Slant height of cone l = √r^2 + h^2
- = √7^2 + 10^2
- = √149
- = 12.2 m
- Area of the floor = π r^2
- = 22/7 x 7 x 7
- = 22 x 7
- = 154 sq m
- Total surface area of the tent = πr (r + l)
- = 22/7 x 7 (7 + 12.2)
- = 22 x 19.2
- = 422.4 sq m
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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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