Question

From a circular disc of radius 10 cm, a rectangle of maximum area is cut. Area of the remaining disc will be

Answer 1

Area of Circle
$= \pi {r}^{2}$
$= \frac{22}{7} \times 10 \times 10$
$= 314.28 {cm}^{2}$

Rectangle of Maximum Area
$= area \: of \: a \: cyclic \: square$

Diagonal of the Square
$= 2 \times 10$
$= 20cm$

Therefore,
By Pythagoras Theorem,
${a}^{2} + {b}^{2} = {c}^{2}$
${2a}^{2} = {20}^{2}$
${2a}^{2} = 400$
${a}^{2} = 200$
$a = \sqrt{200} cm$

Area of Square
$= { \sqrt{200} }^{2}$
$= 200c {m}^{2}$

Therefore,
Area of Remaining Disc
$= 314.28 - 200$
$= 114.28c {m}^{2}$