Inscribed Circle in Square - Circle Radius to Square Area

Level 1

This math topic focuses on finding the area of a square given the radius of an inscribed circle. It forms part of an introductory unit on inscribed squares and circles. The problems provide a radius for the circle inscribed in a square and challenge the student to calculate the corresponding square's area. There are multiple choice answers available for each problem, integrating some complex calculations and use of geometric formulas. The answers represent the areas in various algebraic expressions, making it a practice on both geometry and algebra skills.

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 Area Worksheet

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Inscribed Circle in Square - Circle Radius to Square Area
1
Find the area of the square that has an inscribed circle with radius 2
An svg image showing a math problem
a A LaTex expression showing 16
b A LaTex expression showing 2square root of 4 over 2Pi
c A LaTex expression showing 4 over 2 square root of 2
d A LaTex expression showing 4square root of 8
e A LaTex expression showing {(square root of 8)} to the power of 2 Pi
f A LaTex expression showing 8
2
Find the area of the square that has an inscribed circle with radius 4
An svg image showing a math problem
a A LaTex expression showing 32
b A LaTex expression showing 16Pi
c A LaTex expression showing 2square root of 8 over 2Pi
d A LaTex expression showing {8 over 2 } to the power of 2 Pi
e A LaTex expression showing {32 over 2 } to the power of 2 Pi
f A LaTex expression showing 64
3
Find the area of the square that has an inscribed circle with radius 8
An svg image showing a math problem
a A LaTex expression showing 64
b A LaTex expression showing 128
c A LaTex expression showing 2square root of 32 over 2Pi
d A LaTex expression showing 2square root of 32 over 2
e A LaTex expression showing {128 over 2 } to the power of 2 Pi
f A LaTex expression showing 256
4
Find the area of the square that has an inscribed circle with radius 3
An svg image showing a math problem
a A LaTex expression showing 36
b A LaTex expression showing 9 over Pi
c A LaTex expression showing {18 over 2 } to the power of 2 Pi
d A LaTex expression showing 9 over 2 square root of 2
e A LaTex expression showing {6 over 2 } to the power of 2 Pi
f A LaTex expression showing 18
5
Find the area of the square that has an inscribed circle with radius 6
An svg image showing a math problem
a A LaTex expression showing 144
b A LaTex expression showing 72
c A LaTex expression showing {12 over 2 } to the power of 2 Pi
d A LaTex expression showing 2square root of 36 over 2
e A LaTex expression showing 36
f A LaTex expression showing 72 over Pi
6
Find the area of the square that has an inscribed circle with radius 5
An svg image showing a math problem
a A LaTex expression showing 50
b A LaTex expression showing 13
c A LaTex expression showing 100
d A LaTex expression showing 50 over Pi
e A LaTex expression showing 13 to the power of 2 over 2 Pi
f A LaTex expression showing 13Pi
7
Find the area of the square that has an inscribed circle with radius 7
An svg image showing a math problem
a A LaTex expression showing 196
b A LaTex expression showing 25Pi
c A LaTex expression showing {14 over 2 } to the power of 2 Pi
d A LaTex expression showing 98 over 2 square root of 2
e A LaTex expression showing 98