4. For each problem, decide whether the circumference of the circle or the area of the circle is most useful for finding a solution. Explain your reasoning. a. A car's wheels spin at 1000 revolutions per minute. The diameter of the wheels is inches. You want to know how fast the car is travelling. b. A circular kitchen table has a diameter of 60 inches. You want to know how much fabric is needed to cover the table top. c. A circular puzzle is 20 inches in diameter. All of the pieces are about the same size. You want to know about how many pieces there are in the puzzle. d. You want to know about how long it takes to walk around a circular pond.

Let's analyze each problem to determine whether the **circumference** or the **area** of a circle is most useful for finding the solution. --- **a. A car's wheels spin at 1000 revolutions per minute. The diameter of the wheels is ___ inches. You want to know how fast the car is travelling.** - **Most Useful:** **Circumference** - **Reasoning:** The speed of the car can be determined by calculating the distance the wheel travels in one revolution, which is equal to the circumference of the wheel. By knowing the number of revolutions per minute and the circumference, you can multiply them to find the total distance traveled per minute, thereby determining the car's speed. --- **b. A circular kitchen table has a diameter of 60 inches. You want to know how much fabric is needed to cover the table top.** - **Most Useful:** **Area** - **Reasoning:** To determine the amount of fabric required to cover the table, you need to calculate the surface area of the table top. The area formula \( A = \pi r^2 \) will give you the total surface area that the fabric needs to cover. --- **c. A circular puzzle is 20 inches in diameter. All of the pieces are about the same size. You want to know about how many pieces there are in the puzzle.** - **Most Useful:** **Area** - **Reasoning:** Estimating the number of puzzle pieces involves calculating the total area of the puzzle and then dividing it by the area of an individual piece. Since all pieces are approximately the same size, using the area provides a basis for estimation. --- **d. You want to know about how long it takes to walk around a circular pond.** - **Most Useful:** **Circumference** - **Reasoning:** Walking around the pond involves traversing the perimeter of the circle, which is the circumference. Calculating the circumference will give you the total distance you need to walk, allowing you to estimate the time based on your walking speed. --- In summary: - **Circumference** is most useful for problems **a** and **d**, which involve linear distances around the circle. - **Area** is most useful for problems **b** and **c**, which involve covering a surface or estimating quantities based on surface size.