Question
From a rectangular sheet of paper ABCD with AB = 40cm and AD = 28cm, 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 $= AB = 40cm$
Breadth of a rectangular sheet of paper $= AD = 28cm$
⇒ Area of a rectangular sheet of paper $= AB \times AD = 40 \times 28 = 1120cm^2$
Diameter of a Semicircular portion $= AD = 28cm$
⇒ Radius$ = 14cm$
⇒ 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
$= (1120 - 308)cm^2$
$= 812cm^2$
Breadth of a rectangular sheet of paper $= AD = 28cm$
⇒ Area of a rectangular sheet of paper $= AB \times AD = 40 \times 28 = 1120cm^2$
Diameter of a Semicircular portion $= AD = 28cm$
⇒ Radius$ = 14cm$
⇒ 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
$= (1120 - 308)cm^2$
$= 812cm^2$
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