what is the change in area?

Question

the circumference of a circle is multiplied by 2.4

Answer 1

Hi Lily,

The key to answering this question is to understand the equations for both Circumference and Area of a circle:

C = 2(3.14)r ; where r is the radius.

A = 3.14(r^2)

If the Circumference is multiplied by 2.4, that means that the radius had to increase by 2.4. If the radius increases by 2.4, then the area will increase by 2.4^2, or 5.76

Answer 2

C = 2*PI*R equation for circumference of circle

R = C/(2*PI) solve for Radius

A = PI*R^2 equation for area of circle

A = PI* C^2 substitute for R as a function of circumference

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4 * PI^2

= C^2 reduce fraction

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4*PI

If you multiply C by 2.4, you will increase the area by the square of that or 5.76.