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

2 Answers
May 12, 2018

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%.

May 12, 2018

The area will be reduced by #25%#.

Explanation:

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.