Question

Find the circumference and area of a circle having a diameter of 7 and one half ft.
Use 3.14 for pi.
.
.
.
Question content area right
Part 1
The circumference is
  
enter your response here ft.
​(Round to the nearest tenth as​ needed.)

Answer 1

To find the circumference \( C \) and area \( A \) of a circle with a diameter of \( d = 7.5 \) ft, we can use the following formulas:

1. **Circumference:**
\[
C = \pi \cdot d
\]
2. **Area:**
\[
A = \pi \cdot r^2
\]
where \( r = \frac{d}{2} \) is the radius of the circle.

**Step 1: Calculate the circumference.**

Given:
- Diameter \( d = 7.5 \) ft
- Using \( \pi \approx 3.14 \)

Now, plug in the values:
\[
C = 3.14 \cdot 7.5
\]
\[
C = 23.625 \, \text{ft}
\]

Rounding to the nearest tenth:
\[
C \approx 23.6 \, \text{ft}
\]

**Step 2: Calculate the area.**

First, calculate the radius:
\[
r = \frac{7.5}{2} = 3.75 \, \text{ft}
\]

Now, find the area:
\[
A = 3.14 \cdot (3.75)^2
\]
Calculating \( (3.75)^2 \):
\[
(3.75)^2 = 14.0625
\]
Then:
\[
A = 3.14 \cdot 14.0625 \approx 44.1575 \, \text{ft}^2
\]

Rounding to the nearest tenth:
\[
A \approx 44.2 \, \text{ft}^2
\]

**Summary:**
- **Circumference:** \( 23.6 \) ft
- **Area:** \( 44.2 \) ft²