EXPLANATION:
Give;
We are told of a circle with a central angle measure of 90 degrees. Also the length of the arc formed by the radii is 25 mm.
Required;
We are required to calculate the radius of the circle.
Step-by-step solution;
To solve this problem, we first take note of the formula for calculating the length of an arc, and this is;
[tex]\begin{gathered} LENGTH\text{ }OF\text{ }AN\text{ }ARC: \\ \\ LOA=\frac{\theta}{360}\times2\pi r \end{gathered}[/tex]The variables here are;
[tex]LOA=25,\theta=90\degree,\pi=3.14,r=?[/tex]We can now substitute the known values and we'll have;
[tex]\begin{gathered} 25=\frac{90}{360}\times2\times3.14\times r \\ \\ 25=\frac{1\times2\times3.14\times r}{4} \end{gathered}[/tex]Now we can cross multiply;
[tex]\begin{gathered} \frac{25\times4}{2\times3.14}=r \\ \\ 15.923566879=r \end{gathered}[/tex]We can round this to the nearest hundredth and we now have;
ANSWER:
[tex]Radius=15.92mm[/tex]