Question

if a square is inscribed in a circle, what is the ratio of the areas of the circle and the square? pls give full answer with steps

Answer 1

Diagonal of the square. = Diameter of the circle

diagonal of a sq = √2 a

Radius of the circle = √2 a / 2
= a/√2
area of the circle = π r sq
= π × a / √2 × a/√2
= π a sq / 2
area of sq = a sq

ratio = π a sq / 2× a sq
= π : 2

Answer 2

Answer:

Diagonal of the square. = Diameter of the circle

diagonal of a sq = √2 a

Radius of the circle = √2 a / 2

= a/√2

area of the circle = π r sq

= π × a / √2 × a/√2

= π a sq / 2

area of sq = a sq

ratio = π a sq / 2× a sq

= π : 2