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

Verified

Lets choose r1=4r_1=4. When we half that it means that r2=2r_2=2

A.

C=2πrC=2\pi r Thus

C1=2πr1=2π4=8πC_1=2\pi r_1=2\pi 4=8\pi while C2=2πr2=2π2=4πC_2=2\pi r_2=2\pi 2=4\pi Therefore when we half the radius the circumference also halves

B.

A=πr2A=\pi r^2 Thus A1=πr12=π42=16πA_1=\pi r_1^2=\pi4^2=16\pi while A2=πr22=π22=4πA_2=\pi r_2^2=\pi 2^2=4\pi

Thus when we half the radius we quarter the area.

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