Question

Find the length of cloth used in making a cone of height two times the base radius,
which is square of 2, if the cloth is 100π cm wide.

Answer 1

The length of cloth used in making a cone is 356 cm.

Given:

A cone of height two times the base radius,

which is a square of 2, is made and the cloth is 100π cm wide.

To Find:

The length of cloth used in making a cone.

Solution:

To find the length of cloth used in making a cone we will follow the following steps:

According to the question:

r = 2² = 4 m

h = 2r = 8 m

First, we have to calculate the length of the cone formed,

$l = \sqrt{ {r}^{2} + {h}^{2} } = \sqrt{ {4}^{2} + {8}^{2} } = \sqrt{16 + 64} = \sqrt{80}m = 8.9m$

Now,

Area of cloth used in making the cone = curved surface area of cone = πrl =

$\pi \: \times 4 \times \sqrt{80} = 8.9 \times 4 \times \pi = 35.6\pi \: {m}^{2} = 35.6 \pi\times {10}^{4} {cm}^{2} = 356000\pi{cm}^{2}$

Now,

The cloth is rectangular so, this area of the cloth is the length × breadth which is equal to the area of the cone. so,

Length × breadth of rectangle = 35600π cm²

According to the question:

The breadth of cloth = 100π cm

So,

$length \times 100\pi = 356000\pi$

$length = \frac{356000\pi}{100\pi} = 356 cm$

Henceforth, the length of cloth used in making a cone is 356 cm.

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