Question

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.

	radius (inches)	number of slices
pizza 2	14	6
pizza 3	12	4

slice from pizza 2 slice from pizza 1 slice from pizza 3
□ < □ < □

Explanation:

Step1: Calculate full area of Pizza 1

The area of a full circle is $A = \pi r^2$. For Pizza 1:
$A_1 = \pi (16)^2 = 256\pi$

Step2: Find slice area of Pizza 1

Divide full area by number of slices:
$\text{Slice Area}_1 = \frac{256\pi}{8} = 32\pi$

Step3: Calculate full area of Pizza 2

$A_2 = \pi (14)^2 = 196\pi$

Step4: Find slice area of Pizza 2

$\text{Slice Area}_2 = \frac{196\pi}{6} \approx 32.67\pi$

Step5: Calculate full area of Pizza 3

$A_3 = \pi (12)^2 = 144\pi$

Step6: Find slice area of Pizza 3

$\text{Slice Area}_3 = \frac{144\pi}{4} = 36\pi$

Step7: Compare slice areas

Order from smallest to largest: $32\pi < 32.67\pi < 36\pi$

Answer:

slice from pizza 1 < slice from pizza 2 < slice from pizza 3