calculate circumference and area of a circle given diameter
Check the final answer first, then review the worked steps.
Problem
calculate circumference and area of a circle given diameter
Answer
\((a) 8\pi \text{ cm}, (b) 16\pi \text{ cm}^2\)
Step-by-step solution
- Identify the given information: The problem provides the diameter of the circle, $d = 8 \text{ cm}$. The radius $r$ is half of the diameter, so $r = \frac{d}{2} = \frac{8}{2} = 4 \text{ cm}$.
- Calculate the circumference: The formula for the circumference of a circle is $C = \pi d$ or $C = 2\pi r$. Using the diameter, we get $C = 8\pi \text{ cm}$.
- Calculate the area: The formula for the area of a circle is $A = \pi r^2$. Substituting the radius $r = 4 \text{ cm}$, we get $A = \pi (4)^2 = 16\pi \text{ cm}^2$.