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

Answer 1

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%.

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Answer 2

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.
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Answer 3

If the radius of a circle is reduced by 50 percent, its area is reduced by ( 75 % ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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