NZ Level 6 (NZC) Level 1 (NCEA)

Congruence and Similarity of Circles

We want to compare the circumference and area of two circles: circle A has radius $5$5 units and circle B has radius $40$40 units.

a

What is the circumference of circle A? Give your answer as an exact value.

b

What is the circumference of circle B? Give your answer as an exact value.

c

What is the area of circle A? Give your answer as an exact value.

d

What is the area of circle B? Give your answer as an exact value.

e

By what factor is the radius of circle A enlarged to give the radius of circle B?

f

By what factor is the circumference of circle A enlarged to give the circumference of circle B?

g

By what factor is the area of circle A enlarged to give the area of circle B?

Easy

Approx 5 minutes

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Deduce and apply the angle properties related to circles

Apply geometric reasoning in solving problems