Question

A square of diagonal 8cm is inscribed in a circle. Find the ratio of the areas of the circle and the square

Answer 1

half the dioagonal is radius of circle

radius is 4cm

ratio=1/2×d1×d2/πr^2

1/2×8×8/22/7×4×4

32×4/22×4×4

ratio is 4:11

Answer 2

$\sf\green{Side\:of\:square=\frac{Diagonal}{√2}=\frac{8}{√2}cm}$

$\sf\green{Area\:of\:the\:square={( \frac{8}{ \sqrt{2} }) }^{2}={32cm}^{2}}$

$\large\sf\red{Clearly,}$

$\sf\red{diameter\:of\:the\:circle=}$

$\sf\red{Diagonal\:of\:the\:square=8cm}$

$\therefore$ $\sf{Area\:of\:the\:circle={πr}^{2}=π( { \frac{8}{2} )}^{2}=16π{cm}^{2}}$

$\sf{Hence,the\:area\:of\:the\:shaded\:region}$

$\longrightarrow$$\sf{Area\:of\:the\:circle-Area\:of\:the\:square}$

$\longrightarrow$${\boxed{\sf{(16π-32){cm}^{2}}}}$