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.

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Inscribed Circle in Square - Circle Radius to Square Side Length

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Find the side length of a square that has an inscribed circle with radius 2

r=2

?

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

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Math worksheet on 'Inscribed Circle in Square - Circle Radius to Square Side Length (Level 1)'. Part of a broader unit on 'Inscribed Squares and Circles - Intro' Learn online: app.mobius.academy/math/units/inscribed_squares_and_circles_intro/
1
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 to the power of 2 over 2 Pi
b A LaTex expression showing 4
c A LaTex expression showing {(square root of 8)} to the power of 2 Pi
d A LaTex expression showing 8Pi
e A LaTex expression showing 2square root of 8 over 2Pi
f A LaTex expression showing 8
2
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
b A LaTex expression showing 8Pi
c A LaTex expression showing {4 over 2 } to the power of 2 Pi
d A LaTex expression showing 4Pi
e A LaTex expression showing 2square root of 4 over 2Pi
f A LaTex expression showing 2
3
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 2square root of 25 over 2Pi
b A LaTex expression showing 2square root of 50 over 2Pi
c A LaTex expression showing {50 over 2 } to the power of 2 Pi
d A LaTex expression showing 5
e A LaTex expression showing 10
f A LaTex expression showing 4square root of 50
4
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 14
b A LaTex expression showing 49 over 2 square root of 2
c A LaTex expression showing {(square root of 49)} to the power of 2 Pi
d A LaTex expression showing 7
e A LaTex expression showing 98Pi
f A LaTex expression showing {49 over 2 } to the power of 2 Pi
5
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 2square root of 16 over 2Pi
b A LaTex expression showing 64 over Pi
c A LaTex expression showing 32 over 2 square root of 2
d A LaTex expression showing 16
e A LaTex expression showing 8
f A LaTex expression showing {64 over 2 } to the power of 2 Pi
6
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 2square root of 18 over 2Pi
b A LaTex expression showing 2square root of 72 over 2Pi
c A LaTex expression showing 12
d A LaTex expression showing 4square root of 36
e A LaTex expression showing 6
f A LaTex expression showing 2square root of 12 over 2Pi
7
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 6
b A LaTex expression showing {18 over 2 } to the power of 2 Pi
c A LaTex expression showing {9 over 2 } to the power of 2 Pi
d A LaTex expression showing 18 over 2 square root of 2
e A LaTex expression showing {(square root of 6)} to the power of 2 Pi
f A LaTex expression showing 3