Question

A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7 m and height of the cone is 1 m, what is the area of cloth required​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

463 $m^2$ of the cloth is required to cover the solid object.

Step-by-step explanation:

Given:-

The radius of the cone and the hemisphere, r = 7 m

The height of the cone, h = 1 m

To find:-

The area of the cloth used to cover the solid object.

Step 1 of 2

Since the radius of cone, r = 7 m

And the height of the cone, h = 1 m

Then,

The slant height of the cone is,

l = $\sqrt{h^2+r^2}$

 = $\sqrt{1^2+7^2}$

 = $\sqrt{1+49}$

 = $\sqrt{50}$

l = $5\sqrt{2}$ m

So, the $curved\ surface\ area$ of the cone is,

= $\pi rl$

= $\frac{22}{7}\times 7\times 5\sqrt{2}$

= $110\sqrt{2}$

= 155 $m^2$ (Approx.)

Also, the radius of hemisphere, r = 7 m

So, the $curved\ surface\ area$ of the hemisphere is,

= $2\pi r^2$

= $2\times\frac{22}{7}\times 7^2$

= 308 $m^2$

Step 2 of 2

The area of the cloth required to cover the solid object is,

= The CSA of the cone + The CSA of the hemisphere

= 115 + 308

= 463 $m^2$

Final answer: 463 $m^2$ of the cloth is required to cover the solid object.

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