Once four friends Rahul, Arun,Ajay and Vijay went for a picnic at a hill station. Due to peak season
they did not get proper hotel in the city. The weather was fine so they decided to make a conical tent
at a park. They were carrying 300 2
cloth with them as shown in the fig. Fig. they made tent with
height 10m and diameter 14m. The remaining cloth to make the floor. (Any Four) (One Mark Each)
I) How much cloth was used to make the floor?
a)31.6m2
b) 16 m2
c) 20 m2
d) 10 m2
II) What was the volume of the tent?
a) 300 m2 b) 160 m2
c) 513.3 m2
d) 500 m2
III) What was the area of the floor?
a) 50 m2 b) 100 m2
c) 150 m2
d) 154 m2
IV) What was the T.S.A of the tent?
a)400 m2
b)422 m2
c)300 m2
d) 420 m2
Answers
Answer:
1 b) 16 m2
2 d) 500 m2
3. a) 50 m2 b) 100 m2
4.b)422 m2
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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