This math topic focuses on finding the radius of a circle inscribed within a square, given the square's side length. The problems involve increasingly complex geometry calculations as students compute the radius based on different side lengths (2, 3, 4, 5, and 6). Each problem provides multiple-choice answers, presented as mathematical expressions. This is part of a broader introduction to the geometry of 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 Side Length to Circle Radius Worksheet

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Inscribed Circle in Square - Square Side Length to Circle Radius
1
Find the radius of the circle inscribed in a 3x3 square
An svg image showing a math problem
a A LaTex expression showing 18 over 2 square root of 2
b A LaTex expression showing 3 over 2
c A LaTex expression showing 4square root of 6
d A LaTex expression showing 6 over 2
e A LaTex expression showing 5
f A LaTex expression showing 2square root of 5 over 2Pi
2
Find the radius of the circle inscribed in a 6x6 square
An svg image showing a math problem
a A LaTex expression showing 36 to the power of 2 over 2 Pi
b A LaTex expression showing {18 over 2 } to the power of 2 Pi
c A LaTex expression showing 72 over Pi
d A LaTex expression showing 12 over 2
e A LaTex expression showing 6 over 2
f A LaTex expression showing {72 over 2 } to the power of 2 Pi
3
Find the radius of the circle inscribed in a 4x4 square
An svg image showing a math problem
a A LaTex expression showing 4 over 2
b A LaTex expression showing 16 over 2 square root of 2
c A LaTex expression showing 8 over 2
d A LaTex expression showing 2square root of 16 over 2Pi
e A LaTex expression showing 2square root of 8 over 2
f A LaTex expression showing 16Pi
4
Find the radius of the circle inscribed in a 8x8 square
An svg image showing a math problem
a A LaTex expression showing 2square root of 32 over 2
b A LaTex expression showing 16 over 2
c A LaTex expression showing 64
d A LaTex expression showing 128Pi
e A LaTex expression showing 8 over 2
f A LaTex expression showing 2square root of 128 over 2Pi
5
Find the radius of the circle inscribed in a 2x2 square
An svg image showing a math problem
a A LaTex expression showing 2 over 2
b A LaTex expression showing 4square root of 8
c A LaTex expression showing 4 over 2
d A LaTex expression showing 2
e A LaTex expression showing 2square root of 2 over 2Pi
f A LaTex expression showing 2 to the power of 2 over 2 Pi
6
Find the radius of the circle inscribed in a 7x7 square
An svg image showing a math problem
a A LaTex expression showing 98 over Pi
b A LaTex expression showing 49
c A LaTex expression showing 14 over 2 square root of 2
d A LaTex expression showing 7 over 2
e A LaTex expression showing 14 over 2
f A LaTex expression showing {14 over 2 } to the power of 2 Pi
7
Find the radius of the circle inscribed in a 5x5 square
An svg image showing a math problem
a A LaTex expression showing 10 over 2
b A LaTex expression showing 2square root of 50 over 2Pi
c A LaTex expression showing 2square root of 10 over 2Pi
d A LaTex expression showing 5 over 2
e A LaTex expression showing 13Pi
f A LaTex expression showing {50 over 2 } to the power of 2 Pi