Question

The circumference of the base of a conical tent is 44 m. If the height of the tent is 24 m, find the length of the canvas used in making the tent, if the width of the canvas is 2 m. Also find the cost of canvas at the rate of Rupees 40/m.​

Answer 1

Given :-

• Circumference = 44 m
• Height of the tent = 24 m
• Width of canvas = 2 m

To find :-

• Length of canvas = ?
• Cost of canvas at the rate of ₹40 per m²

Solution :-

It is given that

Circumference = 44 m

➥ 2πr = 44

➜ 2 × 22/7 × r = 44

➝ 44r/7 = 44

➝ 44r = 44 × 7

➝ r = 7 m

∴ Radius = 7 m

For finding the length of canvas used, we need to find out the CSA of cone.

CSA of cone = πrl

But we don't know the value of l i.e slant Height.

For finding Slant Height;

l² = h² + r²

➥ l² = 24² + 7²

➜ l² = 576 + 49

➝ l² = 625

➝ l = √625

➝ l = 25 m

Applying the value of Slant Height in the formula,

CSA of cone = πrl

➝ CSA of cone = 22/7 × 7 × 25

⇒ CSA of cone = 22 × 25

⇒ CSA of cone = 550 m²

∴ CSA of cone = 550 m²

We know that

Area = Length × Breadth

→ 550 = Length × 2

→ Length = 550 ÷ 2

→ Length = 275 m

∴ The length of canvas = 275 m

Cost of canvas:

1 m² = ₹40

550 m² = 550 × 40 = ₹22000

∴ The cost of canvas = ₹22000