Question

From a rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, a semi-circular portion with BC as diameter is cut off. Find the area of remining paper (use π = 22/7)​​

Answer 1

Answer:

here's ur ans⬇

Explanation:

Area of rectangular sheet of paper = Area of rectangle = length × breadth = 40 × 28 = 1120 cm2

Area of semicircular cut out = 1/2 πr2

Area of remaining sheet of paper = Area of rectangular sheet of paper – Area of semicircular cut out.

Therefore, area of remaining sheet of paper is 812 cm2.

Answer 2

$\sf\Large{\underline{\underline{Solution:-}}}$

Step I :-

Finding the area of rectangular sheet.

Where,

• Length = 40 cm
• Breadth = 28 cm

There area:-

${\sf{\green{\boxed{\sf area = {length \: \times breadth}}}}}$

Substitute the values,

$\begin{gathered}\\\;\sf{:\rightarrow\;area\;=\;\bf{{40cm \times 28cm}\:}}\end{gathered}$

$\: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;area\;=\;\bf{{1120cm ^{2} }\:}}\end{gathered}$

∴ Area of rectangular sheet of paper is 1120cm².

⠀

Step ll:-

We know, BC is the diameter of the semi-circle.

Where,

• Diameter (d) = 28cm
• Therefore, Radius (r) = 28 ÷ 2 = 14cm
• Taking π = 22/7 (given)

⠀

${\underline{\underline{\sf{\pink{so,}}}}}$

• Finding the Area of semi-circular cut off from the sheet.

Formula using here,

${\sf{\green{\boxed{\sf area = { \frac{1}{2}\pi \: r^{2} }}}}}$

⠀

On substituting the Values,

$\: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;area\;=\;\bf{{ \frac{1}{2} \times [ \frac{22}{7} \times (14)^{2} ] }\:}}\end{gathered}$

$\: \: \: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;area\;=\;\bf{{ \frac{1}{2} \times [ \frac{22}{7} \times 196] }\:}}\end{gathered}$

$\Longrightarrow$ Cancel 196 by 7, we get

$\: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;area\;=\;\bf{{ \frac{1}{2} \times [{22} \times 28] }\:}}\end{gathered}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;area\;=\;\bf{{ \frac{1}{2} \times {616} }\:}}\end{gathered}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;area\;=\;\bf{{{308cm ^{2} }}\:}}\end{gathered}$

⠀

${\underline{\underline{\sf{\blue{Now,}}}}}$

Area of remaining sheet = Area of rectangular sheet – Area of semi-circular cut off.

= 1120 – 308

= 812

⠀

$\color{pink}{\textbf{\textsf{Required \: Answer}}}$

The area of remaining sheet of paper is 812cm².