Inscribed Square in Circle - Square Area to Circle Area

Level 1

This math topic focuses on calculating the area of a circle with an inscribed square. Problems are given where the area of the square is known, and students are asked to determine the area of the circle. Seven questions are presented, each with a different square area (4, 9, 16, 25, 36, 49, 64). Each question has multiple-choice answers represented in various mathematical expressions and forms involving square roots, powers, and π (pi). The knowledge and skills practiced here include understanding geometric relationships and applying algebraic formulas to find areas.

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 Area Worksheet

Inscribed Square in Circle - Square Area to Circle Area

Find the area of the circle that has a square inscribed of area 9

An svg image showing a math problem

a $A LaTex expression showing \frac{{9}}{2}Pi$

A LaTex expression showing 2square root of 6 over 2Pi

A LaTex expression showing 18 over Pi

A LaTex expression showing 6Pi

A LaTex expression showing {6 over 2 } to the power of 2 Pi

f $A LaTex expression showing \frac{{4} to the power of 2 }{2}Pi$

Find the area of the circle that has a square inscribed of area 36

An svg image showing a math problem

A LaTex expression showing 12Pi

b $A LaTex expression showing \frac{{18} to the power of 2 }{2}Pi$

A LaTex expression showing 2square root of 36 over 2Pi

d $A LaTex expression showing \frac{{36}}{2}Pi$

A LaTex expression showing {36 over 2 } to the power of 2 Pi

A LaTex expression showing 18 over 2 square root of 2

Find the area of the circle that has a square inscribed of area 49

An svg image showing a math problem

A LaTex expression showing 14 to the power of 2 over 2 Pi

A LaTex expression showing 98 over Pi

A LaTex expression showing {49 over 2 } to the power of 2 Pi

A LaTex expression showing {25 over 2 } to the power of 2 Pi

e $A LaTex expression showing \frac{{49}}{2}Pi$

f $A LaTex expression showing \frac{{24} to the power of 2 }{2}Pi$

Find the area of the circle that has a square inscribed of area 4

An svg image showing a math problem

A LaTex expression showing 8Pi

A LaTex expression showing 2square root of 2 over 2Pi

A LaTex expression showing 8 to the power of 2 over 2 Pi

d $A LaTex expression showing \frac{{2} to the power of 2 }{2}Pi$

e $A LaTex expression showing \frac{{4}}{2}Pi$

Find the area of the circle that has a square inscribed of area 64

An svg image showing a math problem

A LaTex expression showing 2square root of 32 over 2Pi

A LaTex expression showing {(square root of 16)} to the power of 2 Pi

c $A LaTex expression showing \frac{{32} to the power of 2 }{2}Pi$

A LaTex expression showing 128 over Pi

A LaTex expression showing {(square root of 32)} to the power of 2 Pi

f $A LaTex expression showing \frac{{64}}{2}Pi$

Find the area of the circle that has a square inscribed of area 16

An svg image showing a math problem

A LaTex expression showing 32Pi

A LaTex expression showing 32

A LaTex expression showing 2square root of 16 over 2Pi

d $A LaTex expression showing \frac{{16}}{2}Pi$

e $A LaTex expression showing \frac{{8} to the power of 2 }{2}Pi$

A LaTex expression showing 32 over 2 square root of 2

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

An svg image showing a math problem

A LaTex expression showing {50 over 2 } to the power of 2 Pi

A LaTex expression showing 25 to the power of 2 over 2 Pi

c $A LaTex expression showing \frac{{12} to the power of 2 }{2}Pi$

A LaTex expression showing {25 over 2 } to the power of 2 Pi

A LaTex expression showing 2square root of 10 over 2Pi

f $A LaTex expression showing \frac{{25}}{2}Pi$