Question

explore 2
part ii: calculating circumference
determine which expressions can be used to calculate the circumference of each pizza
pan needed. use the pizza circumference cards to match each pizza with the equations
that can be used to determine its circumference. write the matching equation that could
be used to calculate the circumference of each pizza. calculate the circumference of
each pizza using 3.14 for π. record the information in the table.
small pizza
radius =
diameter =
circumference equation =
circumference =
medium pizza
radius =
diameter =
circumference equation =
circumference =
large pizza
radius =
diameter =
circumference equation =
circumference =
mega pizza
radius =
diameter =
circumference equation =
circumference =
circles | 153

Explanation:

To solve this, we need the radius or diameter of each pizza. Since they are not provided, we'll assume typical pizza sizes (e.g., small: diameter 10 in, medium: 12 in, large: 14 in, mega: 16 in) for demonstration. The formula for circumference is \( C = \pi d \) or \( C = 2\pi r \) (where \( d \) is diameter, \( r \) is radius, \( \pi \approx 3.14 \)).

Small Pizza (Assume Diameter = 10 in)

Step 1: Find Radius

Radius \( r = \frac{d}{2} = \frac{10}{2} = 5 \) in.

Step 2: Circumference Equation

Using \( C = \pi d \) (or \( C = 2\pi r \)). Let’s use \( C = \pi d \).

Step 3: Calculate Circumference

\( C = 3.14 \times 10 = 31.4 \) in.

Medium Pizza (Assume Diameter = 12 in)

Step 1: Find Radius

\( r = \frac{12}{2} = 6 \) in.

Step 2: Circumference Equation

\( C = \pi d \).

Step 3: Calculate Circumference

\( C = 3.14 \times 12 = 37.68 \) in.

Large Pizza (Assume Diameter = 14 in)

Step 1: Find Radius

\( r = \frac{14}{2} = 7 \) in.

Step 2: Circumference Equation

\( C = \pi d \).

Step 3: Calculate Circumference

\( C = 3.14 \times 14 = 43.96 \) in.

Mega Pizza (Assume Diameter = 16 in)

Step 1: Find Radius

\( r = \frac{16}{2} = 8 \) in.

Step 2: Circumference Equation

\( C = \pi d \).

Step 3: Calculate Circumference

\( C = 3.14 \times 16 = 50.24 \) in.

Filling the Table (with assumed diameters):

Pizza Type	Radius (in)	Diameter (in)	Circumference Equation	Circumference (in)
Medium	6	12	\( C = 3.14 \times 12 \)	37.68
Large	7	14	\( C = 3.14 \times 14 \)	43.96
Mega	8	16	\( C = 3.14 \times 16 \)	50.24

If the actual diameters/radii are different, substitute them into the formula \( C = \pi d \) (or \( C = 2\pi r \)) and recalculate.

Answer:

To solve this, we need the radius or diameter of each pizza. Since they are not provided, we'll assume typical pizza sizes (e.g., small: diameter 10 in, medium: 12 in, large: 14 in, mega: 16 in) for demonstration. The formula for circumference is \( C = \pi d \) or \( C = 2\pi r \) (where \( d \) is diameter, \( r \) is radius, \( \pi \approx 3.14 \)).

Small Pizza (Assume Diameter = 10 in)

Step 1: Find Radius

Radius \( r = \frac{d}{2} = \frac{10}{2} = 5 \) in.

Step 2: Circumference Equation

Using \( C = \pi d \) (or \( C = 2\pi r \)). Let’s use \( C = \pi d \).

Step 3: Calculate Circumference

\( C = 3.14 \times 10 = 31.4 \) in.

Medium Pizza (Assume Diameter = 12 in)

Step 1: Find Radius

\( r = \frac{12}{2} = 6 \) in.

Step 2: Circumference Equation

\( C = \pi d \).

Step 3: Calculate Circumference

\( C = 3.14 \times 12 = 37.68 \) in.

Large Pizza (Assume Diameter = 14 in)

Step 1: Find Radius

\( r = \frac{14}{2} = 7 \) in.

Step 2: Circumference Equation

\( C = \pi d \).

Step 3: Calculate Circumference

\( C = 3.14 \times 14 = 43.96 \) in.

Mega Pizza (Assume Diameter = 16 in)

Step 1: Find Radius

\( r = \frac{16}{2} = 8 \) in.

Step 2: Circumference Equation

\( C = \pi d \).

Step 3: Calculate Circumference

\( C = 3.14 \times 16 = 50.24 \) in.

Filling the Table (with assumed diameters):

Pizza Type	Radius (in)	Diameter (in)	Circumference Equation	Circumference (in)
Medium	6	12	\( C = 3.14 \times 12 \)	37.68
Large	7	14	\( C = 3.14 \times 14 \)	43.96
Mega	8	16	\( C = 3.14 \times 16 \)	50.24

If the actual diameters/radii are different, substitute them into the formula \( C = \pi d \) (or \( C = 2\pi r \)) and recalculate.