Inscribed Square in Circle - Square Side Length to Circle Radius

Level 1

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 7x7 square inscribed
An svg image showing a math problem
a A LaTex expression showing 98
b A LaTex expression showing square root of 49 over 2
c A LaTex expression showing 25 over Pi
d A LaTex expression showing 98 over 2 square root of 2
e A LaTex expression showing square root of 98 over 2
f A LaTex expression showing 2square root of 14 over 2Pi
2
Find the radius of the circle that has a 4x4 square inscribed
An svg image showing a math problem
a A LaTex expression showing 8 over Pi
b A LaTex expression showing square root of 8
c A LaTex expression showing {32 over 2 } to the power of 2 Pi
d A LaTex expression showing {8 over 2 } to the power of 2 Pi
e A LaTex expression showing square root of 16
f A LaTex expression showing 8 over 2 square root of 2
3
Find the radius of the circle that has a 6x6 square inscribed
An svg image showing a math problem
a A LaTex expression showing {36 over 2 } to the power of 2 Pi
b A LaTex expression showing square root of 18
c A LaTex expression showing 12 over Pi
d A LaTex expression showing 18 to the power of 2 over 2 Pi
e A LaTex expression showing square root of 36
f A LaTex expression showing 72Pi
4
Find the radius of the circle that has a 5x5 square inscribed
An svg image showing a math problem
a A LaTex expression showing square root of 25 over 2
b A LaTex expression showing square root of 50 over 2
c A LaTex expression showing 4square root of 10
d A LaTex expression showing 10Pi
e A LaTex expression showing {50 over 2 } to the power of 2 Pi
f A LaTex expression showing 2square root of 25 over 2
5
Find the radius of the circle that has a 2x2 square inscribed
An svg image showing a math problem
a A LaTex expression showing square root of 2
b A LaTex expression showing {8 over 2 } to the power of 2 Pi
c A LaTex expression showing 8 over 2 square root of 2
d A LaTex expression showing square root of 4
e A LaTex expression showing 8Pi
f A LaTex expression showing 2square root of 4 over 2Pi
6
Find the radius of the circle that has a 3x3 square inscribed
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 9 over 2
c A LaTex expression showing 5 over Pi
d A LaTex expression showing 2square root of 5 over 2Pi
e A LaTex expression showing 2square root of 18 over 2
f A LaTex expression showing square root of 18 over 2
7
Find the radius of the circle that has a 8x8 square inscribed
An svg image showing a math problem
a A LaTex expression showing {16 over 2 } to the power of 2 Pi
b A LaTex expression showing 16 over Pi
c A LaTex expression showing 2square root of 128 over 2Pi
d A LaTex expression showing 128 over Pi
e A LaTex expression showing square root of 32
f A LaTex expression showing square root of 64