Question

A square fits exactly inside a circle with each of the vertices being on the circumference of the circle. The square has sides length of X cm. The area of the circle is 56cm^2. Work out the value of x. Give your answer correct to 3sf

Answer 1

Answer: The value of x is 5.970.

Explanation:

Given: The square has sides length of X cm.

Let r be the radius of the circle.

The square fits exactly inside a circle with each of the vertices being on the circumference of the circle.

Then diagonal of square = diameter of circle

i.e.
`√(2)x= 2r` [Diagonal of square =
`√(2)`(side)]

i.e.
`r=(x)/(√(2))`

area of circle =
`\pi r^2`

i.e.
`56=(22)/(7)((x)/(√(2)))^2`

`56=(22)/(7)*(x^2)/(2)\\\\\Rightarrow\ x^2= (7)/(11)*56\\\\\Rightarrow\ x^2=35.636\\\\\Rightarrow\ x=√(35.636)\approx5.970`

Hence, the value of x is 5.970.