If the radius of a circle is increased by 50%, what will be the percent increase in the circumference of the circle?
(Note: The formula for the circumference of a circle is [tex]C = 2\pi r[/tex].)
Answer (2)
The percent increase in the circumference of a circle when the radius is increased by 50% is also 50%.
If the radius of a circle is increased by 50%, we can calculate the percent increase in the circumference of the circle using the circumference formula, C = 2 π r .
Let's denote the original radius as r1 and the new radius as r2.
Using the given information r2 = 1.5r1, since there is a 50% increase in the radius.
The original circumference, C1, is 2 π r 1 , and the new circumference, C2, is 2 π ( 1.5 r 1 ) .
Therefore, C 2 = 2 π ( 1.5 ) r 1
= 3 π r 1 = 1.5 ∗ ( 2 π r 1 )
= 1.5C1.
This shows that the circumference has also been increased by 50%.
When the radius of a circle is increased by 50%, the circumference also increases by 50%. This is determined by comparing the original and new circumferences using the formula for circumference. The percent increase in circumference is therefore 50%.
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