Question

Choose a radius. Draw a circle. What if you halve the radius.

a) What happens to the circumference?

b) What happens to the area

Solution

VerifiedLets choose $r_1=4$. When we half that it means that $r_2=2$

A.

$C=2\pi r$ Thus

$C_1=2\pi r_1=2\pi 4=8\pi$ while $C_2=2\pi r_2=2\pi 2=4\pi$ Therefore when we half the radius the circumference also halves

B.

$A=\pi r^2$ Thus $A_1=\pi r_1^2=\pi4^2=16\pi$ while $A_2=\pi r_2^2=\pi 2^2=4\pi$

Thus when we half the radius we quarter the area.

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