Question

Once 4 students Rahul, Arjun, Ajay & Vijay went for picnic at hill station. They decided

to make a conical tent at park. They were carrying 300 m2

cloth with them. The

height of the tent is 10 meter & diameter is 14 meter. They used the remaining cloth for

the floor

i) How much cloth was used for the floor?

a) 31.6 sq. m b) 16 sq. m

c) 10 sq. m d) 20 sq. m

ii) What was the volume of tent?

a) 300 m cube. B) 160m cube.

c) 513.3 m cube. D) 500 m cube

iii) What was the total surface area of tent?

a) 400 sq. m b) 422.4sq.m

c) 300sq. m d) 400sq. m

iv) What was the area of floor?

a) 50 sq. m b)100 sq. m

c) 150 sq. m d) 154 sq. m​

Answer 1

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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