in the figure given below, AC and BD are two perpendicular diameters o

1.	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» GIVEN :- Diameter of CIRCLE , d = 16 cm. TO FIND :- The area of the shaded region. Perimeter of the shaded region. SOLUTION :- $\\ : \implies \displaystyle \sf \: Radius = \frac{d}{2} \\ \\ \\$ $: \implies \displaystyle \sf \: Radius = \frac{16}{2} \\ \\ \\$ $: \implies \underline{ \boxed{\displaystyle \sf \: Radius = 8 \: cm.}} \\ \\$ ____________________… $\\ \\$ $: \implies \displaystyle \sf \: Area \: of \: shaded \: region = 2 \times \frac{1}{4} \pi r ^{2} \\ \\ \\$ $: \implies \displaystyle \sf \: Area \: of \: shaded \: region = \frac{1}{2} \times 3.14 \times (8) ^{2} \\ \\ \\$ $: \implies \displaystyle \sf \: Area \: of \: shaded \: region = \frac{1}{2} \times 3.14 \times 8 \times 8 \\ \\ \\$ $: \implies \displaystyle \sf \: Area \: of \: shaded \: region = 3.14 \times 4 \times 8 \\ \\ \\$ $: \implies \underline{ \boxed{ \displaystyle \sf \: Area \: of \: shaded \: region = 100.48 \: cm ^{2} }}\\ \\$ ____________________… $\\ \\ \dashrightarrow \displaystyle \sf \: Perimeter\: of \: shaded \: region = 2 \bigg( \frac{1}{4} \times 2\pi r + 2r \bigg) \\ \\ \\$ $\dashrightarrow \displaystyle \sf \: Perimeter\: of \: shaded \: region = 2 \bigg( \frac{1}{2} \times \pi r + 2 r \bigg)\\ \\ \\$ $\dashrightarrow \displaystyle \sf \: Perimeter\: of \: shaded \: region = 2 \bigg( \frac{1}{2} \times 3.14 \times 8 + 2 \times 8 \bigg) \\ \\ \\$ $\dashrightarrow \displaystyle \sf \: Perimeter\: of \: shaded \: region = 2 \bigg( 3.14 \times 4+ 16 \bigg) \\ \\ \\$ $\dashrightarrow \displaystyle \sf \: Perimeter\: of \: shaded \: region = 2 \bigg(12.56 + 16 \bigg) \\ \\ \\$ $\dashrightarrow \displaystyle \sf \: Perimeter\: of \: shaded \: region = 2 \times 28.56 \\ \\ \\$ $\dashrightarrow \underline{ \boxed{ \displaystyle \sf \: Perimeter\: of \: shaded \: region = 57.12 \: cm}} \\$

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»

GIVEN :-

Diameter of CIRCLE , d = 16 cm.

TO FIND :-

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

SOLUTION :-

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

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

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

____________________…

$\\ \\$

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

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

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

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

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

____________________…

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

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

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

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

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

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

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