for each quantity, decide whether circumference or area would be needed to calculate it. Explain or show your reasoning
the amount of paint needed to paint a bullseye
To calculate the amount of paint needed to paint a bullseye, you would need to calculate the area rather than the circumference. Let me explain why.
A bullseye is typically composed of several concentric circles, each with a different color. When you want to paint a surface, you are concerned with covering the entire area of that surface. The paint goes over each of the circular areas making up the bullseye.
The area of a circle is calculated using the formula:
\[ \text{Area} = \pi r^2 \]
where \( \pi \) is a constant (approximately 3.14159) and \( r \) is the radius of the circle.
For each circle in the bullseye, you would calculate the area and then add the areas together to get the total area that needs to be painted. The amount of paint typically depends on this total area and the paint's coverage rate (e.g., how many square meters a liter of paint can cover).
On the other hand, the circumference of a circle, which represents the distance around the circle, is calculated using the formula:
\[ \text{Circumference} = 2\pi r \]
The circumference would tell you the length around the circle, which isn't directly related to the amount of paint needed, as the paint must cover the entire surface area within the circles, not just the edges.
To summarize, for calculating the amount of paint needed for a bullseye, use the area of the circles that make up the bullseye.