Question

Constructed Response Items (MGSE 9-12.G.C. 5) Pizza is often circular shape and size of the pizza is the length of diameter with included crust. A 16 inch pizza is one with a 16 inch diameter. Find following answers and show all steps how you find that answer. (Whole Numbers) A. What is the area of a 16 inch pizza? B. What is the measurement of a central angle for one slice of pizza, if you cut that pizza into 8 equal pieces? C. What is the length of the entire crust of the pizza? D. What is the length of the crust around of two slices of the pizza? (if pizza cut into 8 equal pieces)

Answer 1

`\begin{gathered} \text{Area}_{Pi\text{zza}}=201.06in^2 \\ \text{angle}_{1\text{ slice}}=45\text{ degre}es \\ Length(crust)=50.26\text{ inches} \end{gathered}`

Step-by-step explanation

Step 1

Let

Step 2

A. What is the area of a 16 inch pizza?

the area of a circle is given by.

`\begin{gathered} \text{Area}_(circle)=\pi\cdot((diameter^2)/(4)) \\ \text{Let} \\ \text{diameter}=16\text{ inches} \\ \text{replace} \\ \text{Area}_(circle)=\pi\cdot((16^2)/(4)) \\ \text{Area}_(circle)=\pi64In^2 \\ \text{Area}_{Pi\text{zza}}=201.06in^2 \end{gathered}`

Step 3

B. What is the measurement of a central angle for one slice of pizza

`\begin{gathered} as\text{ the whole circle is 360 degr}ees\text{ , the value for the angle of one slice is} \\ \text{angle}_{1\text{ slice}}=\frac{360\text{ degr}ees}{8}=45\text{ degre}es \\ \text{angle}_{1\text{ slice}}=45\text{ degre}es \end{gathered}`

Step 4

C. What is the length of the entire crust of the pizza?

this length is called Circumference, you can find the Circumference of a circle using:

`\begin{gathered} Circumference=\pi\cdot diameter \\ replace \\ Circumference=\pi\cdot16\text{ inches} \\ \text{Circumference}=50.26\text{ inches} \\ lengthoftheentirecrust=50.26\text{ inches} \end{gathered}`

Step 5

D. What is the length of the crust around of two slices of the pizza?

then,The arc length (D) is:

L = θ × r (when θ is in radians)

A)convert 90 degrees into radians