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Area of Circle, Sector and Segment — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsArea of Circle, Sector and Segment3 Marks
Question
From a rectangular sheet of paper ABCD with $AB = 40\ cm$ and $AD = 28\ cm$, a semicircular portion with BC as diameter is cut off. Find the area of the remaining paper.
✓

Answer

Length of a rectangular sheet of paper $= AB = 40\ cm$
Breadth of a rectangular sheet of paper $= AD = 28\ cm$
$\Rightarrow $ Area of a rectangular sheet of paper $= AB \times AD = 40 \times 28 = 1120\ cm^2$
Diameter of a Semicircular portion $= AD = 28\ cm$
$\Rightarrow $ Radius $= 14\ cm$
⇒ Area of a Semicircular portion $=\frac{1}{2}\times\frac{22}{7}\times14\times14=308\text{cm}^2$
$\therefore$ Area of the remaining paper = Area of a rectangular sheet of paper - Area of a Semicircular portion
$= (1120 - 308)\ cm^2$
$= 812\ cm^2$​​​​​​​

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