Question

what is the area of the circle if the diameter of the circle is 64 square cm?​

Answer 1

area 3216.99

diameter 64

Answer 2

${ \mathcal{{ \color{navy}{\huge{ \fcolorbox{teal}{cyan}{AnSwEr}}}}}} \: \: { \huge{ \color{green} \downarrow}}$

Given the area of the square is

${ \frak{{64cm}^{2}}}$

Then its side will be of length

${ \frak{8cm}}$

Then its diagonal will be of length is

${ \frak{ \sqrt[8]{2}}}$

Since the square is inscribed in a circle then the diagonal of the square will be the diameter of the circle.

Let r be the radius of the circle.

Then 2r =

${ \frak{\sqrt[8]{2}}}$

or, r =

${ \frak{\sqrt[4]{2}}}$

Then the area of the circle =

${πr}^{2} =$

$\frac{22}{7} \times$

${ \frak{( \sqrt[4]{2})^{2}}} =$

$3.14 \times 32 =$

${ \boxed{ \frak{{100.48cm}^{2}}}}$