Question

In the following figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the
(i)quadrant OACB
(ii)shaded region.​

Answer 1

Answer:

The area of quadrant , OACB is 9.625 cm² and area of shaded region is 6.485 cm² .

Step-by-step explanation:

GIVEN :

OA = 3.5 cm , OD = 2 cm

(i) Area of quadrant, OACB , A1 = ¼ × πr²

= ¼ × 22/7 × 3.5 × 3.5

= (11 × 0.5 × 3.5)/2

= (5.5 × 3.5)/2

= 19.25 /2  

= 9.625 cm²

Area of quadrant , OACB = 9.625 cm²

(ii)  

Area of small quadrant ,A2 = ¼ × πr²

= ¼ × 22/7 × 2× 2

= ¼ × 22/7 × 4

= 22/7  

= 3.14 cm²

Area of small quadrant ,A2 = 3.14 cm²

Area of shaded region,A  = Area of quadrant , OACB - Area of small quadrant ,A2

A = A1 - A2

A = 9.625 - 3.14  

A = 6.485 cm²

Area of shaded region = 6.485 cm²

Hence,the area of quadrant , OACB is 9.625 cm² and area of shaded region is 6.485 cm² .

HOPE THIS ANSWER WILL HELP YOU….

Here are more questions of the same chapter :

In the following figure, the square ABCD is divided into five equal parts, all having same area. The central part is circular and the lines AE, GC, BF and HD lie along the diagonals AC and BD of the square. If AB = 22 cm, find:

(i)the circumference of the central part.

(ii)the perimeter of the part ABEF.

https://brainly.in/question/9482181

In the following figure find the area of the shaded region. (Use π = 3.14)

https://brainly.in/question/9483241

Answer 2

$\huge{\underline{\bigstar{\sf{solution!!}}}}$

Given,OACB is a quadrant of a circle

$\large{\sf{Radius = 3.5 =7/2 cm; OD= 2cm}}}$

$\large{\sf{area\: of \: the \: shaded \: region = area \: of \: a \: quadrant \: cricle - area \:of \: triangle \:BOB}}$

=1/4πr²-1/2×b×h

=1/4×22/7×7/2×7/2-1/2×7/2×2

=11×7/2×2×2 -7/2

${\sf{=77/8-7/2}}}$

${\sf{=9.625-3.5}}}$

$\large{\boxed{\sf{=6.125cm2}}}$

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