Inscribed Circle in Square - Circle Radius to Square Side Length

Level 1

This math topic focuses on finding the side length of a square that has an inscribed circle, given the radius of the circle. The topic engages learners in understanding the relationship between the radius of a circle inscribed in a square and the side length of that square. The problems cover multiple instances with different circle radii, challenging the learner to apply geometric principles and algebraic formulas to ascertain the side length of the square corresponding to each given circle radius. This is a fundamental exercise in understanding the properties of inscribed figures and the geometric relations therein.

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

more

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

Mobius Math Academy logo
Inscribed Circle in Square - Circle Radius to Square Side Length
1
Find the side length of a square that has an inscribed circle with radius 7
An svg image showing a math problem
a A LaTex expression showing {25 over 2 } to the power of 2 Pi
b A LaTex expression showing 2square root of 14 over 2
c A LaTex expression showing {(square root of 98)} to the power of 2 Pi
d A LaTex expression showing 7
e A LaTex expression showing 25 over 2 square root of 2
f A LaTex expression showing 14
2
Find the side length of a square that has an inscribed circle with radius 3
An svg image showing a math problem
a A LaTex expression showing 3
b A LaTex expression showing {5 over 2 } to the power of 2 Pi
c A LaTex expression showing 2square root of 9 over 2Pi
d A LaTex expression showing 5
e A LaTex expression showing 4square root of 6
f A LaTex expression showing 6
3
Find the side length of a square that has an inscribed circle with radius 4
An svg image showing a math problem
a A LaTex expression showing 8
b A LaTex expression showing {8 over 2 } to the power of 2 Pi
c A LaTex expression showing {(square root of 16)} to the power of 2 Pi
d A LaTex expression showing 4
e A LaTex expression showing 32 over 2 square root of 2
f A LaTex expression showing 8 over Pi
4
Find the side length of a square that has an inscribed circle with radius 8
An svg image showing a math problem
a A LaTex expression showing 8
b A LaTex expression showing 16
c A LaTex expression showing 2square root of 128 over 2Pi
d A LaTex expression showing 64 over Pi
e A LaTex expression showing {64 over 2 } to the power of 2 Pi
f A LaTex expression showing 128Pi
5
Find the side length of a square that has an inscribed circle with radius 2
An svg image showing a math problem
a A LaTex expression showing {4 over 2 } to the power of 2 Pi
b A LaTex expression showing 4
c A LaTex expression showing 2square root of 4 over 2Pi
d A LaTex expression showing {(square root of 4)} to the power of 2 Pi
e A LaTex expression showing 2
f A LaTex expression showing 4square root of 4
6
Find the side length of a square that has an inscribed circle with radius 5
An svg image showing a math problem
a A LaTex expression showing 10
b A LaTex expression showing 5
c A LaTex expression showing 10 over Pi
d A LaTex expression showing {50 over 2 } to the power of 2 Pi
e A LaTex expression showing 4square root of 50
7
Find the side length of a square that has an inscribed circle with radius 6
An svg image showing a math problem
a A LaTex expression showing {(square root of 18)} to the power of 2 Pi
b A LaTex expression showing 4square root of 36
c A LaTex expression showing 12
d A LaTex expression showing 36 to the power of 2 over 2 Pi
e A LaTex expression showing 4square root of 18
f A LaTex expression showing 6