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[[1]] of length of canvas $2 m$ in width in required to make a conical tent [[2]] the cost of the canvass at the rate of $Rs .80$ per meter.

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Detailed Solution

Given:

The width of the canvas of the tent

w = 2 m

The diameter of the conical tent

d = 20 m

r = d 2 r = 202 r = 10 m

The slant height of the conical tent

l = 42 m

The cost rate of the canvas

= R s . 80 per m

So, the surface area of the conical tent,

⇒ A = π r (r + l)

⇒ A = 227 × 10 × (10 + 42) A = 1634.3 m 2

Also, it is given that only

10 %

This area is allowed for folds and stitching.
The area of the canvas allowed for folds and the stitching

A a l l o w = 10 % o f 1634.3 A a l l o w = 10100 × 1634.3 A a l l o w = 163.43 m 2

So, the total canvas required is the sum of the surface area of the conical tent and the area of the canvas allowed for folds and the stitching.

A a l l o w = A + A a l l o w A a l l o w = 1634.3 + 163.43 A a l l o w = 1797.73 m 2

Now to find the length of the canvas

(l)

, we know that the total area of the canvas is the product of the length and width of the canvas.
So,

A t o t a l = l × w

Solving for the length of the canvas we get,

l = A t o t a l w l = 1797.73 2 l = 898.865 m

So, the cost of canvas for the total length

(l)

of the canvas is given by ,

⇒ C o s t = R s . 80 p e r m × 898.865 m ⇒ C o s t = R s . 71909.2

Therefore, the cost of the canvas is

R s . 71909.2

.
898.865 m of length of canvas

in width in required to make a conical tent

the cost of the canvass at the rate of

per meter.

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