This math topic delves into geometry, specifically focusing on the relationship between the side length of a square inscribed within a circle and the radius of the circle. It comprises multiple problems that require calculating the circle's radius given the side length of the inscribed square. Each question presents a range of potential answers, challenging students to apply geometric principles and mathematical reasoning to find the correct radius corresponding to various square side lengths. This topic serves as a practical exercise for understanding properties of inscribed shapes and relationships within circles.

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

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Inscribed Square in Circle - Square Side Length to Circle Radius Worksheet

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Inscribed Square in Circle - Square Side Length to Circle Radius
1
Find the radius of the circle that has a square inscribed with side length 4
An svg image showing a math problem
a A LaTex expression showing 8 over 2 square root of 2
b A LaTex expression showing {8 over 2 } to the power of 2 Pi
c A LaTex expression showing {32 over 2 } to the power of 2 Pi
d A LaTex expression showing square root of 16
e A LaTex expression showing square root of 8
f A LaTex expression showing 16
2
Find the radius of the circle that has a square inscribed with side length 7
An svg image showing a math problem
a A LaTex expression showing {14 over 2 } to the power of 2 Pi
b A LaTex expression showing square root of 49 over 2
c A LaTex expression showing 49Pi
d A LaTex expression showing 2square root of 49 over 2Pi
e A LaTex expression showing 2square root of 98 over 2Pi
f A LaTex expression showing square root of 98 over 2
3
Find the radius of the circle that has a square inscribed with side length 2
An svg image showing a math problem
a A LaTex expression showing square root of 2
b A LaTex expression showing 4 to the power of 2 over 2 Pi
c A LaTex expression showing 8 over 2 square root of 2
d A LaTex expression showing square root of 4
4
Find the radius of the circle that has a square inscribed with side length 6
An svg image showing a math problem
a A LaTex expression showing {18 over 2 } to the power of 2 Pi
b A LaTex expression showing square root of 18
c A LaTex expression showing 4square root of 72
d A LaTex expression showing square root of 36
e A LaTex expression showing 72 over 2 square root of 2
f A LaTex expression showing 4square root of 12
5
Find the radius of the circle that has a square inscribed with side length 3
An svg image showing a math problem
a A LaTex expression showing 6 to the power of 2 over 2 Pi
b A LaTex expression showing 9 over Pi
c A LaTex expression showing 4square root of 5
d A LaTex expression showing square root of 18 over 2
e A LaTex expression showing 5 over Pi
f A LaTex expression showing square root of 9 over 2
6
Find the radius of the circle that has a square inscribed with side length 5
An svg image showing a math problem
a A LaTex expression showing 2square root of 50 over 2Pi
b A LaTex expression showing {25 over 2 } to the power of 2 Pi
c A LaTex expression showing 2square root of 25 over 2Pi
d A LaTex expression showing square root of 50 over 2
e A LaTex expression showing square root of 25 over 2
f A LaTex expression showing 13 over Pi
7
Find the radius of the circle that has a square inscribed with side length 8
An svg image showing a math problem
a A LaTex expression showing 2square root of 64 over 2
b A LaTex expression showing square root of 64
c A LaTex expression showing square root of 32
d A LaTex expression showing 2square root of 32 over 2
e A LaTex expression showing {64 over 2 } to the power of 2 Pi
f A LaTex expression showing {(square root of 128)} to the power of 2 Pi