The radius of a circle is 10 cm. If the radius is increased by 20%, how do you find the percentage increase in area?

1 Answer
Tony B
Feb 17, 2017

Solution given in a lot of detail so you can see where everything comes from.

Area increase is #44%# of the original area

Explanation:

#color(brown)("Note that the % symbol is like a unit of measurement that is")##color(brown)("worth "1/100)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Setting up the initial condition and change")#

#20%" of "10 = 20/100xx10=2 larr" increase in radius"#

Original area #->pir^2 = pi10^2 = 100pi#

New area #-> pir^2=pi12^2=144pi#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the percentage change")#

Expressing the change as a fraction of the original area we have:

#(144pi-100pi)/(100pi)#

Factor out the #pi# from #144pi-100pi# giving:

#(pi(144-100))/(pixx100)#

This is the same as:

#pi/pixx44/100" "=" "1xx44/100 = 44/100#

This is the same as:

#44xx1/100#

But #1/100# is the same as % so we have:

#44%#

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