Question

Which of the following pairs could be reasonable approximations for the diameter and circumference of a circle? 18 inches and 57 inches 3 centimeters and 28 centimeters 33 meters and 80 meters

Answer 1

First option: 18 inches diameter, 57 inches circumference

Explanation:

Circumference of a circle is...

2 * radius * pi

We can approximate pi (3.14159...) to 3.

So the circumference of a circle is approx.

2 * radius * 3

We know the diameter of a circle is 2 times the radius...

diameter = 2 * radius

Thus, the circumference of a circle is approximately...

diameter * 3

First option:

Diameter 18, circumference 57

Let's try our approximation

18 * 3 = 54

We see that 57 is pretty close and is a reasonable approximation.

Second option:

Diameter 3, circumference 28

3 * 3 = 9

Not even close to 28.

Third option:

Diameter 33, circumference 80

3 * 33 = 99

Closer, but much further off than our first option.

Answer 2

18 inches and 57 inches

Explanation:

The diameter and the circumference of a circle are proportionate to each other.

The circumference of a circle will always be the diameter times
`\pi`. We know this because the circumference of a circle is represented as

`2 \pi r`

Since the diameter is twice the radius, we multiply the radius by 2 - there's already a
`\cdot 2` in this equation, so
`c = \pi d`.

1st option:
`18\cdot3.14 = 56.52`, this is close to 57 so it's reasonable.

2nd option:
`3\cdot 3.14 = 9.42`, this isn't close to 28 at all.

3rd option:
`33 \cdot 3.14 = 103.62`, this isn't close to 80 at all.

So the 1st option is reasonable.

Hope this helped!