# A 5-m-wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used, at the rate of Rs 25 per metre.

Let the length of the cloth used be ‘L’ cm

Area of cloth used = 5 × L eqn1

Also, Given Diameter = d = 14 m and height = h = 24 m

r = 14/2

r = 7 m

Let the slant height of the cone be ℓ m

So, (Slant height)2 = (Height)2 + (Radius)2

Put the values in the above relation

2 = h2 + r2

2 = 242 + 72

2 = 576 + 49

2 = 625

ℓ = √(625)

ℓ = 25 cm eqn1

Also, we know Curved Surface Area of cone = πrℓ

Where r = radius of base, ℓ = slant height

C.S.A = π × 7 × 25 C.S.A = 22 × 25

C.S.A = 550 m2eqn2

Now the Curved surface area of conical tent will be equal to the area of the cloth used to make the tent

C.S.A = Area of cloth

550 = 5 × L (from eqn1 and eqn2) L = 110 m

So, cost of the cloth used = rate of cloth × Length of the cloth

Cost of cloth used = 25 × 110

Cost of cloth = Rs.2750

Cost of the cloth used is Rs. 2750

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