Question

The diameter of a quarter is 24.26 mm and the diameter of a nickel is 21.21 mm. How much bigger is the distance around a quarter than a nickel? (Use 3.14 for Π)

Answer 1

9.577 mm.

Explanation:

We have been given that the diameter of a quarter is 24.26 mm and the diameter of a nickel is 21.21 mm.

Let us find the circumference of quarter and nickel using circumference of circle formula.

`\text{Circumference of circle}=2\pi r`, where r represents radius of the circle.

Since we know that diameter of circle is 2 times its radius, so let us find radius of quarter and nickel by dividing their diameter by 2.

`\text{Radius of quarter}=(24.26)/(2)`

`\text{Radius of quarter}=12.13`

`\text{Radius of nickel}=(21.21)/(2)`

`\text{Radius of nickel}=10.605`

`\text{Circumference of quarter}=2* 3.14* 12.13`

`\text{Circumference of quarter}=76.1764`

Therefore, circumference of quarter is 76.1764 mm.

Let us find circumference of nickel.

`\text{Circumference of nickel}=2* 3.14* 10.605`

`\text{Circumference of nickel}=66.5994`

Let us subtract circumference of nickel from circumference of quarter.

`\text{The difference between distance around quarter and nickel}=76.1764-66.5994`

`\text{The difference between distance around quarter and nickel}=9.577`

Therefore, the distance around a quarter is 9.577 millimeters bigger than a nickel.