Q. 284.4( 5 Votes )

# 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.

Answer :

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

∴ Radius = r = D/2

⇒ 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

⇒ ℓ^{2} = h^{2} + r^{2}

⇒ ℓ^{2} = 24^{2} + 7^{2}

⇒ ℓ^{2} = 576 + 49

⇒ ℓ^{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 m^{2}→eqn2

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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