Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

In the figure given below O is the centre of the circle and OPQR is a rectangle, A is a point on PO such that $AO = \frac{1}{3} PO$ and B is the mid-point of OR. Find the area of the shaded region, if PA = 8 cm and BR = 4cm $(Use π = 3.14) .$

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

132.68 {cm}^{2}

121.12 {cm}^{2}

108.56 {cm}^{2}

None of these

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given,

AO = \frac{1}{3} PO

Also, B is the mid-point of OR,

PA = 8 cm

BR = 4 cm

From figure,

PO = PA + AO

PO = PA + \frac{PO}{3}

\frac{2 PO}{3} = PA = 8

PO = 12 cm

Now again from figure,

OR = OB + BR = 2 BR

OR = 2 \times 4

OR = 8 cm

OB = BR = 4 cm

Now, the area of shaded region,
A= area of rectangle OPQR +

\frac{3}{4}

(area of circle)-

\frac{1}{4}

(area of circle)

A = PO \times OR + \frac{3}{4} π {(OB)}^{2} - \frac{1}{4} π {(OB)}^{2}

A = 12 \times 8 + \frac{3}{4} π {(4)}^{2} - \frac{1}{4} π {(4)}^{2}

A = 96 + 3 \times 3.14 \times 4 - 3.14 \times 4

A = 121.12 {cm}^{2}

This is the required area.
Correct option is 2

Watch 3-min video & get full concept clarity