Question

From a circular metal sheet of radius 9 cm, a circle of radius 4 cm is removed. Find the area of the
remaining sheet. (Take n = 3.14)​

Answer 1

Step-by-step explanation:

Just calculate the area of the circle with radius 9 and 4 cm,and and subtract the area of 4 cm circle from 9 cm circle.

Answer 2

Given -

• Radius of metal sheet = 9cm

• Radius of circle = 4cm

To find -

• Area of remaining sheet.

Formula used -

• Area of circle

Solution -

In the question, we are provided with the radius of 2 circles, and we need to find the area remaining sheet, for that first we will find the area of 1st circle and then the area of 2nd circle, and then we will subract area of 2st circle from 2nd circle, that will give us the area of the remaining sheet. Let's do it!

So -

Let's find the area of the first circle, by using the formula of area of circle.

$\sf \underline{area \: of \: circle} \: = \pi \: {r}^{2}$

Where -

π = 3.14 (as per the requirement of question)

r = radius = 9cm

On substituting the values -

$\sf \: Area = \pi \: {r}^{2}$

$\sf \: Area = 3.14 \times {(9cm)}^{2}$

$\sf \: Area = 3.14 \times 81cm$

$\sf \: Area = 254.34 \: {cm}^{2}$

Similarly -

We will find the area of the 2nd circle, by the same formula.

$\sf \underline{area \: of \: circle} \: = \pi \: {r}^{2}$

Where -

π = 3.14

r = radius = 4cm

On substituting the values -

$\sf \: Area = \pi \: {r}^{2}$

$\sf \: Area \: = 3.14 \times {(4cm)}^{2}$

$\sf \: Area \: = 3.14 \times 16cm$

$\sf \: Area \: =50.24 {cm}^{2}$

Now -

We will find the area of the remaining sheet, by subtracting, the area of 1st circle from the area of 2nd circle.

$\sf \underline{area \: of \: remaining \: sheet} \: = area \: of \: 1st \: circle \: - area \: of \: 2nd \: circle$

On substituting the values -

$\sf \: Area_{(remaining\:sheet)} = 254.34 - 50.25$

$\sf \: Area_{(remaining\:sheet)} \: = 204.1 {cm}^{2}$

$\therefore$ Area of the remaining sheet is 204.1 cm²

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