Answer:
[tex]\begin{gathered} a)\text{ 0.7 cm} \\ b)\text{ it will be shorter as the circle with radius 6 cm is larger} \\ c)\text{ 1.05 cm} \end{gathered}[/tex]Explanation:
a) Here, we want to get the length of the arc
Mathematically, we can calculate that using the formula:
[tex]L\text{ = }\frac{\theta}{360}\text{ }\times\text{ 2}\pi r[/tex]where r is the radius of the circle which is 5 cm
theta is the central angle subtended by the arc which is 10 degrees
Substituting the values, we have it that:
[tex]L\text{ = }\frac{10}{360}\text{ }\times\text{ 2}\times3.142\text{ }\times\text{ 4 = 0.70 cm}[/tex]b) The arc will be shorter than the one on a circle with a radius of 6 cm
The reason for this is that a circle with a radius of 6 cm will be larger than one with a radius of 4 cm
c) Here, we want to find the length if the radius was 6 cm
We simply substitute for the radius and the central angle as we have done in (a)
We have that as:
[tex]\begin{gathered} L\text{ = }\frac{10}{360}\times2\times3.142\text{ }\times\text{ 6} \\ \\ L\text{ = 1.05 cm} \end{gathered}[/tex]