Question
A pizza has a diameter of 16 inches.
(2 points)
7th Grade Math Formula Sheet
Part 1. What is the circumference, in inches, of the pizza, rounded to the nearest hundredth? Use 3.14 for π
.
Circumference =
inches
Part 2. What is the area, in square inches, of the pizza, rounded to the nearest hundredth? Use 3.14 for π
.
Area =
square inches
Answers
GPT-4o mini
To solve the problem, we'll use the formulas for the circumference and area of a circle.
### Part 1: Circumference
The formula for the circumference \( C \) of a circle is given by:
\[
C = \pi \times d
\]
where \( d \) is the diameter.
Given the diameter of the pizza is 16 inches:
\[
C = 3.14 \times 16
\]
Calculating that:
\[
C = 50.24 \text{ inches}
\]
So, the circumference, rounded to the nearest hundredth, is:
\[
\text{Circumference} = 50.24 \text{ inches}
\]
### Part 2: Area
The formula for the area \( A \) of a circle is given by:
\[
A = \pi \times r^2
\]
where \( r \) is the radius. The radius is half of the diameter.
Given the diameter is 16 inches, the radius \( r \) is:
\[
r = \frac{d}{2} = \frac{16}{2} = 8 \text{ inches}
\]
Now we can calculate the area:
\[
A = 3.14 \times (8^2) = 3.14 \times 64
\]
Calculating that:
\[
A = 200.96 \text{ square inches}
\]
So, the area, rounded to the nearest hundredth, is:
\[
\text{Area} = 200.96 \text{ square inches}
\]
### Final Answers:
- Circumference = 50.24 inches
- Area = 200.96 square inches
### Part 1: Circumference
The formula for the circumference \( C \) of a circle is given by:
\[
C = \pi \times d
\]
where \( d \) is the diameter.
Given the diameter of the pizza is 16 inches:
\[
C = 3.14 \times 16
\]
Calculating that:
\[
C = 50.24 \text{ inches}
\]
So, the circumference, rounded to the nearest hundredth, is:
\[
\text{Circumference} = 50.24 \text{ inches}
\]
### Part 2: Area
The formula for the area \( A \) of a circle is given by:
\[
A = \pi \times r^2
\]
where \( r \) is the radius. The radius is half of the diameter.
Given the diameter is 16 inches, the radius \( r \) is:
\[
r = \frac{d}{2} = \frac{16}{2} = 8 \text{ inches}
\]
Now we can calculate the area:
\[
A = 3.14 \times (8^2) = 3.14 \times 64
\]
Calculating that:
\[
A = 200.96 \text{ square inches}
\]
So, the area, rounded to the nearest hundredth, is:
\[
\text{Area} = 200.96 \text{ square inches}
\]
### Final Answers:
- Circumference = 50.24 inches
- Area = 200.96 square inches