Question

what is a reasonable estimate for the area of a circle with radius 2 cm? a. 6 centimeters squared c. 12 centimeters squared b. 9 centimeters squared d. 16 centimeters squared

Answer 1

Answer: 12 cm²

Work Shown

`A = \pi*r^2\\\\A \approx 3.14*2^2\\\\A \approx 12.56\\\\`

The closest of the answer choices is 12 cm²

The steps will vary slightly depend on what value you use for pi.

For instance, if we had pi = 3.14159, then,

`A = \pi*r^2\\\\A \approx 3.14159*2^2\\\\A \approx 12.56636\\\\`

It means that as pi gets more accurate, so does the area.

If we go the opposite direction and get less accurate with pi, then we could use the approximation pi = 3.

If we go this route then:

`A = \pi*r^2\\\\A \approx 3*2^2\\\\A \approx 12\\\\`

This could be what your teacher has in mind.