Question

A circle is drawn inside a square so its circumference touches each of the four sides of the

square. If the area of the circle is 125.8cm2 calculate the length of the sides of the square.

Answer 1

12.66 cm

Explanation:

Area of the circle = 125.8 Sq cm

`\therefore \: \pi {r}^(2) = 125.8 \\ \\ \therefore \: 3.14 * {r}^(2) = 125.8 \\ \\ {r}^(2) = (125.8)/(3.14) \\ \\ {r}^(2) = 40.0636943 \\ \\ {r} = √(40.0636943) \\ \\ r = 6.32958879 \\ \\ r \approx \: 6.33 \: cm \\ \\ d \: = 2r \\ \\ d = 2 * 6.33 \\ \\ d = 12.66 \: cm \\`

Diameter of the circle = 12.66 cm

Since, circumference of the circle touches each of the four sides of the square.

So, length of the sides of the square

= diameter of the circle.

= 12.66 cm