11. Once four friends Rahul, Arun, Ajay and Vijay went for a picnic at a hill station. Due to peak season, they didn`t 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 300m2 cloth with them. As shown in the figure they made the tent with height 10m and diameter 14m. The remaining cloth was used for the floor. 10m 14m (i) (ii) (iii) (iv) (v) How much cloth was used for the floor? (a) 31.6m2 (b)16m2 (c) 10m2 (d)20m2 What was the volume of the tent? (a)300m3 (b)160m3 (c)513.3m3 (d)500m3 What was the area of the floor? (a)50m2 (b)100m2 (c)150m2 (d)154m2 What was the T.S.A of the tent? (a)400m2 (b)422.4m2 (c)300m2 (d)400m2 What was the slant height of the tent? (a)12cm (b)12.2cm (c)15cm (d)17cm
Answers
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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Answer:
1 -a
2-b
3-b
4-c
5-d
Step-by-step explanation:
hope it's helpful