If the radius of a circle is reduced by 50 percent, by what percent is its area reduced?

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Answer 1 · 2018-05-12T00:55:02

Area goes with the square of radius, so if we multiply the radius by $.5$ we multiply the area by $.5^2=.25,$ a reduction of 75%.

Answer 2 · 2018-05-12T00:56:28

The area will be reduced by $25%$ .

Example 1

A circle has a radius of $"4 cm"$ . If the radius is reduced by $50%$ , what is the new area? By what percent is its area reduced?

Radius $"4.0 cm"$

$A=pir^2$

$A=pi*("4.0 cm")^2="50.3 cm"$

Radius $"2.0 cm"$

$A=pi*("2.0 cm")^2="12.6 cm"^2"$

Percent reduction of area

$(12.6color(red)cancel(color(black)("cm"^2)))/(50.3color(red)cancel(color(black)("cm"^2)))xx100="25.0%$

Example 2

A circle has radius of $"24 cm"$ . If the radius is reduced by $50%$ , what is the new area? By what percent is its area reduced?

Radius $"24.0 cm"$

$A=pi*(24.0"cm")^2="1809.6 cm"^2"$

Radius $"12.0 cm"$

$A=pi*("12.0 cm")^2="452.4 cm"^3"$

Percent reduction of area

$(452.4color(red)cancel(color(black)("cm"^2)))/(1809.6color(red)cancel(color(black)("cm"^2)))xx100="25.0%"$

I used the $pi$ key on my calculator.