SOLUTION: Hi A square of area 70cm^2 is inscribed inside a circle . What is the area of the circle Thank you

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Question 1201695: Hi
A square of area 70cm^2 is inscribed inside a circle . What is the area of the circle
Thank you
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52782) About Me  (Show Source):
You can put this solution on YOUR website!
.
A square of area 70cm^2 is inscribed inside a circle . What is the area of the circle
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If the area of a square is 70 cm^2, then its side  "a"  is  a = sqrt%2870%29 cm.


Then the radius of the circle is  r = sqrt%28%28a%2F2%29%5E2%2B%28a%2F2%29%5E2%29 = sqrt%28%282a%5E2%29%2F4%29 = a%2Fsqrt%282%29 = sqrt%2870%29%2Fsqrt%282%29.


Then the area of the circle is  

    area = pi%2Ar%5E2 = pi%2A%2870%2F2%29 = 35%2Api = 35%2A3.14 = 109.9 cm^2  (approximately).    ANSWER

Solved.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

The square has area 70 square cm.
The side length is sqrt%2870%29 cm.


For each right triangle, the hypotenuse is the diameter of the circle.
r = radius
2r = diameter = hypotenuse
Use the pythagorean theorem to find that hypotenuse+=+2r+=+sqrt%28140%29
Or you could use the 45-45-90 triangle template to connect the leg length to the hypotenuse.


Then it leads to
r+=+sqrt%28140%29%2F2

The area of the circle is then...
A+=+pi%2Ar%5E2

A+=+pi%2A%28sqrt%28140%29%2F2%29%5E2

A+=+pi%2A%28%28%28sqrt%28140%29%29%5E2%29%2F%282%5E2%29%29

A+=+pi%2A%28140%2F4%29

A+=+pi%2A35

A+=+35pi

The exact area of the circle is 35pi square cm.

If you use the approximation pi = 3.14, then the approximate area of the circle would be 35*pi = 35*3.14 = 109.9 square cm.