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
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Answers
GPT-4o mini
To solve the problems, we can use the formulas for circumference and area of a circle.
### Part 1: Circumference
The formula for the circumference \(C\) of a circle is:
\[
C = \pi \times d
\]
where \(d\) is the diameter.
Given that the diameter of the pizza is 16 inches, we can substitute this into the formula:
\[
C = 3.14 \times 16
\]
Calculating this:
\[
C = 50.24
\]
So the circumference of the pizza, rounded to the nearest hundredth, is:
\[
C = 50.24 \text{ inches}
\]
### Part 2: Area
The formula for the area \(A\) of a circle is:
\[
A = \pi \times r^2
\]
where \(r\) is the radius. The radius is half of the diameter, so:
\[
r = \frac{d}{2} = \frac{16}{2} = 8 \text{ inches}
\]
Now we can substitute the radius into the area formula:
\[
A = 3.14 \times 8^2
\]
Calculating \(8^2\):
\[
8^2 = 64
\]
Now substitute back into the area formula:
\[
A = 3.14 \times 64
\]
Calculating this:
\[
A = 200.96
\]
So the area of the pizza, rounded to the nearest hundredth, is:
\[
A = 200.96 \text{ square inches}
\]
### Summary
- **Circumference:** 50.24 inches
- **Area:** 200.96 square inches
### Part 1: Circumference
The formula for the circumference \(C\) of a circle is:
\[
C = \pi \times d
\]
where \(d\) is the diameter.
Given that the diameter of the pizza is 16 inches, we can substitute this into the formula:
\[
C = 3.14 \times 16
\]
Calculating this:
\[
C = 50.24
\]
So the circumference of the pizza, rounded to the nearest hundredth, is:
\[
C = 50.24 \text{ inches}
\]
### Part 2: Area
The formula for the area \(A\) of a circle is:
\[
A = \pi \times r^2
\]
where \(r\) is the radius. The radius is half of the diameter, so:
\[
r = \frac{d}{2} = \frac{16}{2} = 8 \text{ inches}
\]
Now we can substitute the radius into the area formula:
\[
A = 3.14 \times 8^2
\]
Calculating \(8^2\):
\[
8^2 = 64
\]
Now substitute back into the area formula:
\[
A = 3.14 \times 64
\]
Calculating this:
\[
A = 200.96
\]
So the area of the pizza, rounded to the nearest hundredth, is:
\[
A = 200.96 \text{ square inches}
\]
### Summary
- **Circumference:** 50.24 inches
- **Area:** 200.96 square inches