Question

from a circular aluminium sheet of radius 28cm, two circles of radius 3.5cm and a rectangle of length 5cm and breadth 2cm are removed. find the area of the remaining sheet.

Answer 1

Answer:

Area of remaining sheet = 2377 cm²

Step-by-step explanation:

Given:

• Radius of aluminium sheet = 28 cm
• Two circles of radii 5 cm and a rectangle of length 5 cm and breadth 5 cm is removed from it.

To Find:

• Area of the remaining sheet

Solution:

First finding the area of the circular aluminum sheet.

Area of a circle is given by

Area of a circle = π r²

where r is the radius

Substitute the data,

Area of aluminium sheet = 22/7 × 28 × 28

Area of the aluminium sheet = 2464 cm²

Now finding the area of the smaller circles cut from it,

Area of smaller circles = 2 × 22/7 × 3.5 × 3.5

Area of smaller circles = 77 cm²

Area of a rectangle is given by,

Area of a rectangle = length × breadth

Hence,

Area of the rectangle cut from it = 5 × 2 = 10 cm²

Now area of the remaining sheet is given by,

Area of remaining sheet = Area of aluminium sheet - ( Area of the two circles + Area of the rectangle)

Substituting the data,

Area of remaining sheet = 2464 - (77 + 10) = 2464 - 87

Area of the remaining sheet = 2377 cm²

Hence area of the remaining sheet is 2377 cm².

Answer 2

Step-by-step explanation:

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$\text{\Large\underline{\red{Question:-}}}$

:$\Longrightarrow$ ● From a circular aluminium sheet of radius 28cm, two circles of radius 3.5cm and a rectangle of length 5cm and breadth 2cm are removed. find the area of the remaining sheet.

$\text{\Large\underline{\orange{To\ find:-}}}$

$\sf To\ find = \begin{cases} \sf{●\ In\ this\ question\ we\ have\ to\ find\ the\ area\ of\ the\ remaining\ sheet.} \end{cases}$

$\text{\Large\underline{\green{Given:-}}}$

$\sf Given = \begin{cases} \sf\pink{●\ Radius\ of\ the\ aluminium\ sheet\ =\ 28cm.} \\ \\ \sf\pink{●\ Two\ circles\ of\ radii\ 5cm\ and\ a\ rectangle\ of\ length\ 5cm\ and\ the\ breadth\ 5cm\ is\ removed\ from\ it.} \end{cases}$

$\text{\Large\underline{\purple{Solution:-}}}$

First:-

● We find the area of the circular aluminium sheet.

● $\sf\fbox{Area\ of\ circle\ =\ π\ r²}$

Here:-

● Here "R" is the radius.

By substituting the values, we get:-

● $\sf{Area_{aluminium\ sheet}\ =\ \dfrac{22}{7}\ ×\ 28\ ×\ 28}$

● $\sf{Area_{aluminium\ sheet}\ =\ 2464cm²}$

Now:-

● We find the area of smaller circles cut from it,

● $\sf{Area_{smaller\ circles}\ =\ 2\ ×\ \dfrac{22}{7}\ ×\ 3.5\ ×\ 3.5}$

● $\sf{Area_{smaller\ circles}\ =\ 77cm²}$

$\sf{Area_{rectangle}\ =\ length\ ×\ breadth}$

So:-

● $\sf{Area_{of\ rectangle\ cut\ from\ it}\ =\ 5\ ×\ 2\ =\ 10cm²}$

Now area of remaining sheet:-

● $\sf{Area\ of\ remaining\ sheet\ =\ Area\ of\ aluminium\ sheet\ -\ (Area\ of\ the\ two\ circles\ +\ Area\ of\ the\ rectangle).}$

● $\sf{Area_{remaining\ sheet}\ =\ 2464\ -\ (77\ +\ 10)\ =\ 2464\ -\ 87}$

● $\sf{Area_{remaining\ sheet}\ =\ 2377cm².}$

Hence:-

● The area of the remaining sheet is 2377cm².

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