Respuesta :
Answer:
9.577 mm.
Step-by-step 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.
[tex]\text{Circumference of circle}=2\pi r[/tex], 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.
[tex]\text{Radius of quarter}=\frac{24.26}{2}[/tex]
[tex]\text{Radius of quarter}=12.13[/tex]
[tex]\text{Radius of nickel}=\frac{21.21}{2}[/tex]
[tex]\text{Radius of nickel}=10.605[/tex]
[tex]\text{Circumference of quarter}=2\times 3.14\times 12.13[/tex]
[tex]\text{Circumference of quarter}=76.1764[/tex]
Therefore, circumference of quarter is 76.1764 mm.
Let us find circumference of nickel.
[tex]\text{Circumference of nickel}=2\times 3.14\times 10.605[/tex]
[tex]\text{Circumference of nickel}=66.5994[/tex]
Let us subtract circumference of nickel from circumference of quarter.
[tex]\text{The difference between distance around quarter and nickel}=76.1764-66.5994[/tex]
[tex]\text{The difference between distance around quarter and nickel}=9.577[/tex]
Therefore, the distance around a quarter is 9.577 millimeters bigger than a nickel.
