Drag each tile to the correct box.
Paul orders 3 different sizes of pizzas. Each pizza is cut into equal-sized slices as described in the table. Put the pizzas in order by the area of a slice from smallest area to largest area.
\begin{tabular}{|c|c|c|}
\cline { 2-3 } \multicolumn{1}{c|}{} & Radius (inches) & Number of Slices \\
\hline Pizza 1 & 16 & 8 \\
\hline Pizza 2 & 14 & 6 \\
\hline Pizza 3 & 12 & 4 \\
\hline
\end{tabular}
slice from pizza 2
slice from pizza 3
slice from pizza 1
$\square$ < $\square$ < $\square$
Answer (1)
Calculate the area of each pizza using the formula A = π r 2 .
Divide the area of each pizza by the number of slices to find the area of one slice.
Calculate the area of one slice for Pizza 1: 32 π ≈ 100.53 square inches.
Calculate the area of one slice for Pizza 2: 3 98 π ≈ 102.63 square inches, and for Pizza 3: 36 π ≈ 113.10 square inches. The order is: slice from pizza 1 < slice from pizza 2 < slice from pizza 3 .
Explanation
Problem Analysis Let's analyze the problem. We have three pizzas with different radii and different numbers of slices. Our goal is to determine the area of a single slice for each pizza and then order the pizzas from the smallest slice area to the largest slice area.
Solution Strategy To find the area of a single slice, we first need to calculate the total area of each pizza using the formula for the area of a circle, which is A = π r 2 , where r is the radius of the pizza. Then, we divide the total area by the number of slices to find the area of one slice.
Calculate Area of Pizza 1 Slice For Pizza 1, the radius is 16 inches and there are 8 slices. The total area of Pizza 1 is: A 1 = π ( 1 6 2 ) = 256 π The area of one slice of Pizza 1 is: 8 256 π = 32 π ≈ 100.53 square inches
Calculate Area of Pizza 2 Slice For Pizza 2, the radius is 14 inches and there are 6 slices. The total area of Pizza 2 is: A 2 = π ( 1 4 2 ) = 196 π The area of one slice of Pizza 2 is: 6 196 π = 3 98 π ≈ 102.63 square inches
Calculate Area of Pizza 3 Slice For Pizza 3, the radius is 12 inches and there are 4 slices. The total area of Pizza 3 is: A 3 = π ( 1 2 2 ) = 144 π The area of one slice of Pizza 3 is: 4 144 π = 36 π ≈ 113.10 square inches
Compare and Order the Slice Areas Now, we compare the areas of the slices: Pizza 1: 32 π ≈ 100.53 square inches Pizza 2: 3 98 π ≈ 102.63 square inches Pizza 3: 36 π ≈ 113.10 square inches
Ordering these from smallest to largest, we get: Pizza 1 < Pizza 2 < Pizza 3
Final Answer Therefore, the order of the pizzas by the area of a slice from smallest to largest is: slice from pizza 1 < slice from pizza 2 < slice from pizza 3.
Examples
Understanding area calculations is crucial in many real-world scenarios. For instance, when planning a garden, you need to calculate the area of different sections to determine how much soil or fertilizer to use. Similarly, when designing a room layout, knowing the area of the furniture and the room helps in optimizing the space. These calculations ensure efficient use of resources and space, whether in gardening, interior design, or even urban planning.
