Inscribed Circle in Square - Square Area to Circle Radius

Level 1

This math topic focuses on finding the radius of a circle that is inscribed within a square, given the area of the square. Each question presents different square areas, ranging from 4 to 49, and requires calculating the corresponding inscribed circle's radius. Multiple choice answers are provided for each problem, with the format suggesting a need for understanding and applying geometric relationships and formulas, notably the relationship between the side length of the square and the diameter of the inscribed circle. This includes some calculations with square roots and rationalizing denominators. This topic is part of an introduction to inscribed squares and circles.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Inscribed Circle in Square - Square Area to Circle Radius Worksheet

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Inscribed Circle in Square - Square Area to Circle Radius
1
Find the radius of the circle inscribed in a square of area 25
An svg image showing a math problem
a A LaTex expression showing 2square root of 13 over 2Pi
b A LaTex expression showing \frac{square root of 25}{2}
c A LaTex expression showing 2square root of 50 over 2
d A LaTex expression showing {50 over 2 } to the power of 2 Pi
e A LaTex expression showing 2square root of 25 over 2Pi
f A LaTex expression showing \frac{square root of 12}{2}
2
Find the radius of the circle inscribed in a square of area 4
An svg image showing a math problem
a A LaTex expression showing {8 over 2 } to the power of 2 Pi
b A LaTex expression showing \frac{square root of 2}{2}
c A LaTex expression showing 8 to the power of 2 over 2 Pi
d A LaTex expression showing 4 over Pi
e A LaTex expression showing \frac{square root of 4}{2}
f A LaTex expression showing {2 over 2 } to the power of 2 Pi
3
Find the radius of the circle inscribed in a square of area 36
An svg image showing a math problem
a A LaTex expression showing \frac{square root of 36}{2}
b A LaTex expression showing 72 over Pi
c A LaTex expression showing \frac{square root of 18}{2}
d A LaTex expression showing 4square root of 72
e A LaTex expression showing {72 over 2 } to the power of 2 Pi
f A LaTex expression showing 4square root of 36
4
Find the radius of the circle inscribed in a square of area 9
An svg image showing a math problem
a A LaTex expression showing \frac{square root of 4}{2}
b A LaTex expression showing \frac{square root of 9}{2}
c A LaTex expression showing {9 over 2 } to the power of 2 Pi
d A LaTex expression showing 4square root of 18
e A LaTex expression showing 6 to the power of 2 over 2 Pi
f A LaTex expression showing 2square root of 6 over 2Pi
5
Find the radius of the circle inscribed in a square of area 16
An svg image showing a math problem
a A LaTex expression showing \frac{square root of 8}{2}
b A LaTex expression showing 4square root of 32
c A LaTex expression showing \frac{square root of 16}{2}
d A LaTex expression showing 32Pi
e A LaTex expression showing 16 over Pi
f A LaTex expression showing 2square root of 8 over 2Pi
6
Find the radius of the circle inscribed in a square of area 64
An svg image showing a math problem
a A LaTex expression showing {(square root of 64)} to the power of 2 Pi
b A LaTex expression showing 32
c A LaTex expression showing 4square root of 16
d A LaTex expression showing \frac{square root of 32}{2}
e A LaTex expression showing \frac{square root of 64}{2}
f A LaTex expression showing 4square root of 32
7
Find the radius of the circle inscribed in a square of area 49
An svg image showing a math problem
a A LaTex expression showing {(square root of 98)} to the power of 2 Pi
b A LaTex expression showing \frac{square root of 24}{2}
c A LaTex expression showing \frac{square root of 49}{2}
d A LaTex expression showing 4square root of 98
e A LaTex expression showing 2square root of 98 over 2Pi
f A LaTex expression showing 49Pi