Answer:
Step-by-step explanation:
To find the area of a circle with a circumference of 25.12 mm, we can substitute the circumference into the circumference formula to find the radius, then substitute the radius into the area of a circle formula.
The formula for the circumference of a circle with radius r is C = 2πr.
Given that C = 25.12 and π = 3.14, then:
[tex]25.12=2\cdot 3.14 \cdot r\\\\\\25.12=6.28r\\\\\\r=\dfrac{25.12}{6.28}\\\\\\r=4\; \sf mm[/tex]
Therefore, the radius of the circle is 4 millimeters.
Now, substitute r = 4 and π = 3.14 into the area of a circle formula A = πr², and solve for A:
[tex]A=3.14 \cdot 4^2\\\\\\A=3.14 \cdot 16\\\\\\A=50.24\; \rm mm^2[/tex]
So, the area of the circle that has a circumference of 25.12 mm is:
[tex]\LARGE\boxed{\boxed{50.24\; \rm mm^2}}[/tex]
