Question

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 1

ANSWER

Let the slant height of the cone be 'l' meters.

height =24 m and diameter =14 m or radius =7 m.

Then according to the question.

l²=h²+r²

l

2

=24

2

+7

2

l

2

=576+49

l

2

=625

l=

625

m

l=25 m

So, the slant height of the cone is 25 m.

Now,

Curved Surface Area of the cone =πrl=

7

22

×7×25

CSA=550m

2

Now, length of the cloth used = Area/ width of the cloth$$= \dfrac{550}{5}$$

Length of the cloth used =110m

Cost of cloth =Rs.25/meter

Total cost of clothe used 25×110=Rs.2750

Answer 2

✬ Total cost = Rs 2750 ✬

Step-by-step explanation:

Given:

• Width of cloth is 5 m.
• Diameter of tent is 14 m.
• Height of tent is 24 m.
• Rate of cloth per m is Rs 25.

To Find:

• Total cost of cloth ?

Solution: Let's find the radius (r) and slant height (l) of the tent.

➯ Diameter = 2 × Radius

➯ 14 = 2r

➯ 7 m = radius

and

➯ Slant height = √height² + radius ²

➯ l = √24² + 7²

➯ l = √576 + 49 = √625 = 25 m

Now to find the cloth used, we need to find the CSA of conical tent.

As we know that

★ CSA of Cone = πrl square units ★

$\implies{\rm }$ CSA = 22/7 × 7 × 25

$\implies{\rm }$ 22 × 25

$\implies{\rm }$ 550 m²

• So length of cloth required = Area/width

• Length of cloth = 550/5 = 110 m

➮ For 1 metre, cost of cloth is Rs 25.

∴ For 10 m, cost of cloth will be

➮ Rs 25 × 110 = Rs 2750

Hence, total cost of cloth used in making conical tent will be Rs 2750.