Find the area and circumference of a circle with diameter 6 mm. Write answers in te...
Check the final answer first, then review the worked steps.
Problem
Find the area and circumference of a circle with diameter 6 mm. Write answers in terms of pi and include units.
Answer
Area: $9\pi$ mm$^2$, Circumference: $6\pi$ mm
Step-by-step solution
- Identify the given information: The problem provides the diameter of the circle, which is $d = 6$ mm.
- Calculate the radius: The radius ($r$) of a circle is half of its diameter. So, $r = \frac{d}{2} = \frac{6 \text{ mm}}{2} = 3$ mm.
- Calculate the area: The formula for the area ($A$) of a circle is $A = \pi r^2$. Substitute the radius we found into the formula: $A = \pi (3 \text{ mm})^2 = \pi (9 \text{ mm}^2) = 9\pi$ mm$^2$.
- Calculate the circumference: The formula for the circumference ($C$) of a circle is $C = \pi d$ or $C = 2\pi r$. Using the diameter: $C = \pi (6 \text{ mm}) = 6\pi$ mm. Alternatively, using the radius: $C = 2\pi (3 \text{ mm}) = 6\pi$ mm.
- State the final answers: The area of the circle is $9\pi$ mm$^2$ and the circumference is $6\pi$ mm.