Question

Circles of radii 3.5 cm are cut out from a square piece of an aluminium sheet of side
28 cm. Find the total number of circles which can be made. Also, find the area of
aluminium sheet which got wasted.
​

Answer 1

${\boxed{ \sf{Given}}}$

• Radii of circles = 3.5 cm

• Side of square sheet = 28cm

${ \boxed{ \sf{To \: Find}}}$

• Number of circles

• Area of sheet, that got wasted.

${ \boxed {\sf{Solution}}}$

In the question, we are provided with the radii of the circles and the side of a square sheet and we need to find the number of circles that can be made from that square sheet, and also we need to find the area of wasted sheet. So, for that, first we will find the area of square and then the area of circle, then we will divide both the areas, that will give us the number of circles. After that, for finding the area of wasted sheet, we will deduct the area of square from the area of circle. Let's do it!

So -

First let's find the area of square, by applying the formula of area of square, by squaring the given side.

$\sf \underline{area\: of \: square} \: = {(side)}^{2}$

On substituting the values -

$\sf \: Area \: = {(side)}^{2}$

$\sf \: Area \: = {(28 \: cm)}^{2}$

$\sf \: Area \: = 784 \: cm^{2}$

Similarly -

We will find the area of the circle, by applying the formula of area of circle, for that we should have radius, which we have.

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

On substituting the values -

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

$\sf \: Area \: = \dfrac{22}{7} \times {(3.5 \: cm)}^{2}$

$\sf \: Area \: = \dfrac{22}{7} \times 12.25 \: cm$

$\sf \: Area \: = 22 \: \times 1.75 \: cm$

$\sf \: Area \: = 38.5 \: {cm}^{2}$

Now -

We will find the number of circles, by dividing the area of square by the area of circle.

$\sf \: Number_{(of\:circles)} \: = \dfrac{area \: of \: square}{area \: of \: circle}$

$\sf \: Number_{(of\:circles)} \: = \dfrac{784}{38.5}$

$\sf \: Number_{(of\:circles)} = \: 21 \: (approx)$

At the end -

We will find the area of wasted sheet, by deducting the area of square from the area of circle.

$\sf \: Area_{(of\:wasted\:sheet)} \: = area \: of \: sheet \: - \: area \: of \: circle$

$\sf \: Area_{(of\:wasted\:sheet)} = \: 784 \: - \: 38.5$

$\sf \: Area_{(of\:wasted\:sheet)} \: = 748.2 \: {cm}^{2}$

________________________________________________________

Answer 2

Answer:

• Radii of circles = 3.5 cm
• Side of square sheet = 28cm

ToFind

Number of circles

Area of sheet, that got wasted.

Solution

In the question, we are provided with the radii of the circles and the side of a square sheet and we need to find the number of circles that can be made from that square sheet, and also we need to find the area of wasted sheet. So, for that, first we will find the area of square and then the area of circle, then we will divide both the areas, that will give us the number of circles. After that, for finding the area of wasted sheet, we will deduct the area of square from the area of circle. Let's do it!

So -

First let's find the area of square, by applying the formula of area of square, by squaring the given side.

area of square

=(side) 2

On substituting the values -

Area=(side) 2

Area=(28cm)2

Area=784cm 2

Similarly -

We will find the area of the circle, by applying the formula of area of circle, for that we should have radius, which we have.

area of circle

=πr2

On substituting the values -

Area =

$|\pi r ^{2}$

Area= 7/22 ×(3.5cm)

Area= 22

Area=38.5cm

Now -

We will find the number of circles, by dividing the area of square by the area of circle.

areaofcircle

areaofsquare

Number of circles

= 38.5784

Number of circles

=21(approx)

At the end -

We will find the area of wasted sheet, by deducting the area of square from the area of circle.

Area of wasted sheet

=areaofsheet−areaofcircle

Area of wasted sheet

=784−38.5

Area of wasted sheet: = 748.2cm