Solution:
a) Given a circle of diameter, d, 10mm.
To find the area, A, of a circle, the formula is
[tex]\begin{gathered} A=\pi r^2 \\ Where\text{ }\pi\text{ is taken as 3.14} \\ r\text{ is the radius of the circle} \\ r=\frac{d}{2}=\frac{10}{2}=5\text{ mm} \end{gathered}[/tex]Substitute 5 for r into the formula to find the area, A, of a circle.
[tex]\begin{gathered} A=\pi r^2 \\ A=3.14\times5^2=3.14\times25=78.5\text{ mm}^2 \\ A=78.5\text{ mm}^2 \end{gathered}[/tex]Hence, the area, A, of the circle is 78.5 mm²
To find the circumference, C, of the circle, the formula is
[tex]\begin{gathered} C=2\pi r \\ C=2\times3.14\times5=31.4\text{ mm} \\ C=31.4\text{ mm} \end{gathered}[/tex]Hence, the circumference, C, of the circle is 31.4 mm
Thus, the answers are
[tex]78.5,31.4[/tex]b) Given a circle of radius, r, is 6 in
To find the area, A, of a circle, the formula is
[tex]\begin{gathered} A=\pi r^2 \\ A=3.14\times6^2=3.14\times36=113.04\text{ in}^2 \\ A=113.04\text{ in}^2 \end{gathered}[/tex]Hence, the area, A, of the circle is 113.04 in²
To find the circumference, C, of the circle, the formula is
[tex]\begin{gathered} C=2\pi r \\ C=2\times3.14\times6=37.68\text{ in} \end{gathered}[/tex]Hence, the circumference, C, of the circle is 37.68 in
Thus, the answers are
[tex]113.04,37.68[/tex]