Answer

Verified

405.3k+ views

**Hint:**A closed cylinder has three faces on its surface, the curved surface of the cylindrical portion, and the two circular planes closing the two open sides of the curved surface. We can calculate the total surface area by adding the area of these individual faces.

**Complete Step by Step Solution:**

Let us calculate the areas of the individual faces of the closed cylinder of radius 7 m and height 3 m.

The curved surface area ${{A}_{1}}$ of the cylinder will be equal to height times the circumference of the curvature. If r is the radius and h is the height of the cylinder, the curved surface area will be given by the below equation.

$\Rightarrow {{A}_{1}}=\text{circumference}\times \text{height}$

We know that the circumference of a circle is equal to $2\pi r$.

$\Rightarrow {{A}_{1}}=2\pi r\times h=2\pi rh$

Now let us substitute the radius and height in the above equation.

$\Rightarrow {{A}_{1}}=2\pi rh=2\pi \times \text{7 m}\times \text{3 m}$

$\Rightarrow {{A}_{1}}=2\pi \times 21=131.9\text{5 }{{\text{m}}^{2}}$

The area of the two circular planes covering the open ends of the curved surface will be equal to

$\Rightarrow {{A}_{2}}=2\times \pi {{r}^{2}}$

Substituting the value of radius in the above equation, we get

$\Rightarrow {{A}_{2}}=2\times \pi \times {{\left( \text{7 m} \right)}^{2}}=307.8\text{8 }{{\text{m}}^{\text{2}}}$

The total surface area, A of the closed cylinder will be

$\Rightarrow A={{A}_{1}}+{{A}_{2}}$

$\Rightarrow A=131.9\text{5 }{{\text{m}}^{2}}+307.8\text{8 }{{\text{m}}^{\text{2}}}=439.8\text{3 }{{\text{m}}^{\text{2}}}$

**Hence the area of the metal sheet required to make a closed cylinder of radius 7 m and height 3 m is**

$\Rightarrow A=439.8\text{3 }{{\text{m}}^{\text{2}}}\simeq 44\text{0 }{{\text{m}}^{\text{2}}}$.

$\Rightarrow A=439.8\text{3 }{{\text{m}}^{\text{2}}}\simeq 44\text{0 }{{\text{m}}^{\text{2}}}$.

**Note:**

In this problem, they have mentioned that the given cylinder is a closed cylinder. Therefore we have to consider the circular areas covering the open ends. But if the surface area of an open cylinder is asked, we should calculate only the area of the curved surface of the cylinder which is $A=2\pi rh$, given r is the radius and h is the height of the cylinder.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Give a reason for the establishment of the Mohammedan class 10 social science CBSE

What are the two main features of Himadri class 11 social science CBSE

The continent which does not touch the Mediterranean class 7 social science CBSE

India has form of democracy a Direct b Indirect c Presidential class 12 sst CBSE

which foreign country is closest to andaman islands class 10 social science CBSE

One cusec is equal to how many liters class 8 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which foreign country is closest to Andaman Islands class 11 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE