Inscribed Square in Circle - Square Area to Circle Radius (Level 1)

This math topic focuses on calculating the radius of circles that have squares inscribed within them, using the given areas of the squares. Each question presents a scenario where the area of the square inscribed within a circle is known, and the task is to determine the circle's radius. The problems involve various mathematical expressions and calculations to deduce the radius from the area of the square. This set of problems is a part of broader learning units on inscribed shapes, particularly concerning squares and 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 Area to Circle Radius

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Find the radius of the circle that has a square inscribed with area 25

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Inscribed Square in Circle - Square Area to Circle Radius Worksheet

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Math worksheet on 'Inscribed Square in Circle - Square Area to Circle Radius (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 radius of the circle that has a square inscribed with area 4
An svg image showing a math problem
a A LaTex expression showing 4 to the power of 2 over 2 Pi
b A LaTex expression showing 4
c A LaTex expression showing 8 over 4 square root of 2
d A LaTex expression showing {(square root of 4)} to the power of 2 Pi
e A LaTex expression showing {4 over 2 } to the power of 2 Pi
f A LaTex expression showing 4 over 4 square root of 2
2
Find the radius of the circle that has a square inscribed with area 25
An svg image showing a math problem
a A LaTex expression showing 10 over 2 square root of 2
b A LaTex expression showing 50 over 4 square root of 2
c A LaTex expression showing {(square root of 13)} to the power of 2 Pi
d A LaTex expression showing 2square root of 10 over 2Pi
e A LaTex expression showing 25 over 4 square root of 2
f A LaTex expression showing 50Pi
3
Find the radius of the circle that has a square inscribed with area 16
An svg image showing a math problem
a A LaTex expression showing 8 over 2 square root of 2
b A LaTex expression showing 16 over 4 square root of 2
c A LaTex expression showing 32 over 4 square root of 2
d A LaTex expression showing 32 over Pi
e A LaTex expression showing 32Pi
f A LaTex expression showing 32 to the power of 2 over 2 Pi
4
Find the radius of the circle that has a square inscribed with area 64
An svg image showing a math problem
a A LaTex expression showing 128 over 4 square root of 2
b A LaTex expression showing 64 over 4 square root of 2
c A LaTex expression showing 2square root of 128 over 2Pi
d A LaTex expression showing {32 over 2 } to the power of 2 Pi
e A LaTex expression showing {16 over 2 } to the power of 2 Pi
f A LaTex expression showing 2square root of 16 over 2
5
Find the radius of the circle that has a square inscribed with area 49
An svg image showing a math problem
a A LaTex expression showing 49 over 4 square root of 2
b A LaTex expression showing 98 over 4 square root of 2
c A LaTex expression showing 2square root of 25 over 2Pi
d A LaTex expression showing 2square root of 25 over 2
e A LaTex expression showing {14 over 2 } to the power of 2 Pi
f A LaTex expression showing 49
6
Find the radius of the circle that has a square inscribed with area 9
An svg image showing a math problem
a A LaTex expression showing 9 over 4 square root of 2
b A LaTex expression showing 18 over 4 square root of 2
c A LaTex expression showing {9 over 2 } to the power of 2 Pi
d A LaTex expression showing 9 to the power of 2 over 2 Pi
e A LaTex expression showing 2square root of 9 over 2
f A LaTex expression showing 2square root of 18 over 2
7
Find the radius of the circle that has a square inscribed with area 36
An svg image showing a math problem
a A LaTex expression showing 72 over 4 square root of 2
b A LaTex expression showing 36 over 4 square root of 2
c A LaTex expression showing 36 over Pi
d A LaTex expression showing {36 over 2 } to the power of 2 Pi
e A LaTex expression showing {(square root of 18)} to the power of 2 Pi
f A LaTex expression showing 12 to the power of 2 over 2 Pi