Question

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

Answer 1

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)`
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`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`

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`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%`