What is the difference in area between a circle with a diameter of 3 meters and a square with a side length of 3 meters?

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What is the difference in area between a circle with a diameter of 3 meters and a square with a side length of 3 meters?

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Answer 1 · 2016-02-01T19:31:12

$1.931 m^{2}$ $1.931"m"^2$

Explanation:

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The formulas for the area of a circle with diameter $d$ $d$ and the area of a square with side length $d$ $d$ are;

$A_{circle} = π r^{2} = π {(\frac{d}{2})}^{2} = \frac{π}{4} d^{2}$ $A_"circle" = pi r^2 = pi (d/2)^2 = pi/4 d^2$

$A_{square} = d^{2}$ $A_"square" = d^2$

To find the difference, we can subtract the area of the circle from the area of the square.

$A_{square} - A_{circle} = d^{2} - \frac{π}{4} d^{2}$ $A_"square" - A_"circle"= d^2 - pi/4 d^2$

$= (1 - \frac{π}{4}) d^{2}$ $= (1-pi/4)d^2$

This is the general formula for the difference in the areas. Plugging in $3 m$ $3"m"$ for the diameter gives a value of;

$(1 - \frac{π}{4}) {(3 m)}^{2} = 1.931 m^{2}$ $(1-pi/4)(3"m")^2 = 1.931"m"^2$

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What is the difference in area between a circle with a diameter of 3 meters and a square with a side length of 3 meters?

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