Question

In figure, AOBCA represents a quadrant of a circle of radius $3.5$cm with centre O. Calculate the area of the shaded portion (Take $\pi =\frac{22}{7}$)

• A. $2.156c{m}^2$
• B. $4.653c{m}^2$
• C. $6.125c{m}^2$
• D. None of these
  

Answer 1

The correct option is C $6.125c{m}^2$

We are given that radius of the quadrant =$3.5$cm

$\therefore$ Area of the quadrant AOBCA

$=\frac{1}{4}\pi r^2$

$=\frac{1}{4}\times \frac{22}{7}\times (3.5{)}^2$

$=9.625c{m}^2$

Area of the triangle AOD

$=\frac{1}{2}\times base\times height$

$=\frac{1}{2}\times OA\times OD$

$=\frac{1}{2}\times 3.5\times 2c{m}^2$

$=3.5c{m}^2$

Hence Area of the shaded region =Area of the quadrant-Area of the triangle AOD

$=9.625-3.5$

$=6.125c{m}^2$