Inscribed Circle in Square - Circle Area to Square Area

Level 1

This math topic focuses on finding the area of a square when an inscribed circle's area is given. It involves using geometric formulas relating the circle's area to the square's side length. By applying the formula for the area of a circle and properties of inscribed shapes, students calculate the corresponding area of the square. The problems increase in difficulty by presenting circles with different areas, requiring students to manipulate algebraic expressions to solve for the square's area. Multiple choice answers apply various algebraic and geometric expressions for solution verification.

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

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Inscribed Circle in Square - Circle Area to Square Area Worksheet

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Inscribed Circle in Square - Circle Area to Square Area
1
Find the area of the square that has an inscribed circle of area 7
An svg image showing a math problem
a A LaTex expression showing {(square root of 25)} to the power of 2 Pi
b A LaTex expression showing {(square root of 49)} to the power of 2 Pi
c A LaTex expression showing 2square root of 49 over 2Pi
d A LaTex expression showing 14 over Pi
e A LaTex expression showing 2square root of 14 over 2Pi
f A LaTex expression showing 28 over Pi
2
Find the area of the square that has an inscribed circle of area 4
An svg image showing a math problem
a A LaTex expression showing 8 over Pi
b A LaTex expression showing {16 over 2 } to the power of 2 Pi
c A LaTex expression showing 16Pi
d A LaTex expression showing 16 over Pi
e A LaTex expression showing 16 over 2 square root of 2
f A LaTex expression showing 2square root of 32 over 2Pi
3
Find the area of the square that has an inscribed circle of area 2
An svg image showing a math problem
a A LaTex expression showing 4 over Pi
b A LaTex expression showing 2Pi
c A LaTex expression showing 8 over Pi
d A LaTex expression showing 4Pi
e A LaTex expression showing 2square root of 4 over 2
4
Find the area of the square that has an inscribed circle of area 6
An svg image showing a math problem
a A LaTex expression showing 12
b A LaTex expression showing 4square root of 36
c A LaTex expression showing 2square root of 72 over 2Pi
d A LaTex expression showing 24 over Pi
e A LaTex expression showing 72
f A LaTex expression showing 12 over Pi
5
Find the area of the square that has an inscribed circle of area 5
An svg image showing a math problem
a A LaTex expression showing 20 over Pi
b A LaTex expression showing 10 over Pi
c A LaTex expression showing 13 over Pi
d A LaTex expression showing 4square root of 13
e A LaTex expression showing 10Pi
f A LaTex expression showing 2square root of 25 over 2Pi
6
Find the area of the square that has an inscribed circle of area 8
An svg image showing a math problem
a A LaTex expression showing 16 over Pi
b A LaTex expression showing 32 over Pi
c A LaTex expression showing 32 over 2 square root of 2
d A LaTex expression showing 64 to the power of 2 over 2 Pi
e A LaTex expression showing {32 over 2 } to the power of 2 Pi
f A LaTex expression showing 128 over Pi
7
Find the area of the square that has an inscribed circle of area 3
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 {9 over 2 } to the power of 2 Pi
c A LaTex expression showing 6 over Pi
d A LaTex expression showing 18
e A LaTex expression showing {6 over 2 } to the power of 2 Pi
f A LaTex expression showing 12 over Pi