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
⇒ ℓ2 = h2 + r2
⇒ ℓ2 = 242 + 72
⇒ ℓ2 = 576 + 49
⇒ ℓ2 = 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 m2→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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