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If the diameter of a circle is increased by 6 cm, what is the increase in the circumference of the circle?

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Answer:

The circumference will be larger by 3 cm.

Step-by-step explanation:

We know that the circumference of a circle is C = 2πr, where r is the radius. The circumference can also be expressed as C = 2π [tex]\frac{d}{2}[/tex], where d is the diameter (since the radius is half the diameter).

So, if we increase the diameter by 6:

C = 2π [tex]\frac{(d+6)}{2}[/tex]

C = 2π [tex]\frac{d}{2}+\frac{6}{2}[/tex]

C = 2π [tex]\frac{d}{2}[/tex] + 3

If we compare this to the original equation, C = 2π [tex]\frac{d}{2}[/tex], we see that if we increase the diameter by 6 cm, the circumference will be larger by 3 cm.

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