Question

A paper is in the form of a rectangle PQRS in which PQ = 10 cm and QR = 7 cm . two semi circular portions with QR and PS as diameter are cut off . find the area of the remaining part.... Please answer this guy's .....​

Answer 1

Answer:

Area of remaining part =Area of rectangle area of semi circle

=lb-2πr^2/2

=(10) (7) -2(22/7) (3.5) ^2/2)

=70-38.5

=31.5cm²

Therefore the area of the remaining part is 31.5cm²

Answer 2

Given :

• PQRS is a rectangle with ,

1. PQ = 10cm
2. QR = 7cm

• 2 semi-circle are cut , with diameter = QR and PS

To find :

Area of remaining part

Formula used :

• Area of rectangle = length × Breadth
• Area of semi-circle = (1/2)πr²

Solution :

First of all find area of rectangular paper PQRS

area of PQRS = PQ × QR

area of PQRS = 10 × 7 = 70cm

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Now find area of semi-circle.

• Radius of semi-circle = Diameter ÷ 2 = QR ÷ 2

Radius of semi-circle = 7/2 cm

• Radius of other semi-circle = PS ÷ 2

{ As opposite side of triangle are equal , QR = PS }

Radius of other semi-circle = 7/2 cm

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$\sf \implies \: Area \: of \: semicircle \: = \: \dfrac{1}{2} \times \dfrac{22}{7} \times { (\dfrac{7}{2}) }^{2} \\ \\ \sf \implies \: Area \: of \: semicircle \: = \: \dfrac{1}{2} \: \times 22 \times 7 \times \dfrac{1}{4} \\ \\ \sf \implies \: Area \: of \: semicircle \: = \: \: 19.25 {cm}^{2}$

Therefore , area of Two semi-circle = 19.25 × 2

Area of two semi-circle = 38.5 cm²

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Area of remaining part = Area of rectangle - Area of two semi-circle

Area of remaining part = 70 - 38.5

Area of remaining part = 31.5 cm²

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ANSWER :

Area of remaining part = 31.5 cm²