Question

The figure given shows a rectangle with a semicircle and 2 identical quadrants inside it. What is the shaded area of the figure? (Use = 22/7 ) * Captionless Image 363 cm² 259 cm² 305 cm² 216 cm²​

Answer 1

259 $cm^{2}$

Given:

The area of hemisphere of radius ($r_{1}$) = 14 cm

The area of two identical quadrants ($r_{2}$) = 7 cm

Solution:

($A_{1}$) Area of rectangle = length x breadth  = (28 x 23) $cm^{2}$ = 644 $cm^{2}$

($A_{2}$) Area of hemisphere = π$r_{1}^{2}$ / 2 = $\frac{22}{7}$ x $\frac{14^{2} }{2}$ = 308 $cm^{2}$

($A_{3}$) Area of two identical quadrants = 2 x π $r_{2}^{2}$ / 4 = $\frac{22}{7}$ x $\frac{7^{2} }{4}$ = 77 $cm^{2}$

The area of the shaded portion is,

A = [ $A_{1}$ - ($A_{2}$ + $A_{3}$) $cm^{2}$

A = [ 644 - ( 308 + 77) $cm^{2}$

A = [ 644 - 385 ] $cm^{2}$

A = 259 $cm^{2}$