Question

in the figure given below, AC and BD are two perpendicular diameters of a circle with centre O. If AC= 16 cm, calculate the area and perimeter of the shaded region (take pi= 3.14)​

Answer 1

Answer:

Given radius of circle is 8cm

Ar. Of shaded part

= πr + 4r

= 3.14 × 8 + 4 × 8

= 25.12 + 32

= 57.12 cm

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Answer 2

GIVEN :-

• Diameter of Circle , d = 16 cm.

TO FIND :-

• The area of the shaded region.
• Perimeter of the shaded region.

SOLUTION :-

$\\ : \implies \displaystyle \sf \: Radius = \frac{d}{2}$

$: \implies \displaystyle \sf \: Radius = \frac{16}{2}$

$: \implies \underline{ \boxed{\displaystyle \sf \: Radius = 8 \: cm.}}$

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$: \implies \displaystyle \sf \: Area \: of \: shaded \: region = 2 \times \frac{1}{4} \pi r ^{2}$

$: \implies \displaystyle \sf \: Area \: of \: shaded \: region = \frac{1}{2} \times 3.14 \times (8) ^{2}$

$: \implies \displaystyle \sf \: Area \: of \: shaded \: region = \frac{1}{2} \times 3.14 \times 8 \times 8$

$: \implies \displaystyle \sf \: Area \: of \: shaded \: region = 3.14 \times 4 \times 8$

$: \implies \underline{ \boxed{ \displaystyle \sf \: Area \: of \: shaded \: region = 100.48 \: cm ^{2} }}$

____________________…

$\\ \\ \dashrightarrow \displaystyle \sf \: Perimeter\: of \: shaded \: region = 2 \bigg( \frac{1}{4} \times 2\pi r + 2r \bigg)$

$\dashrightarrow \displaystyle \sf \: Perimeter\: of \: shaded \: region = 2 \bigg( \frac{1}{2} \times \pi r + 2 r \bigg)$

$\dashrightarrow \displaystyle \sf \: Perimeter\: of \: shaded \: region = 2 \bigg( \frac{1}{2} \times 3.14 \times 8 + 2 \times 8 \bigg)$

$\dashrightarrow \displaystyle \sf \: Perimeter\: of \: shaded \: region = 2 \bigg( 3.14 \times 4+ 16 \bigg)$

$\dashrightarrow \displaystyle \sf \: Perimeter\: of \: shaded \: region = 2 \bigg(12.56 + 16 \bigg)$

$\dashrightarrow \displaystyle \sf \: Perimeter\: of \: shaded \: region = 2 \times 28.56$

$\dashrightarrow \underline{ \boxed{ \displaystyle \sf \: Perimeter\: of \: shaded \: region = 57.12 \: cm}}$