Question

Express the required calculation in terms of pi and then round to the nearest tenth.
How much fencing is required to enclose a circular garden whose radius is 21 ​meters?
Question content area bottom
Part 1
There are
  
enter your response here
▼
m
m squared
of fencing required.
​(Simplify your answer. Type an exact answer in terms of pi​.)
Part 2
There are approximately
  
enter your response here
▼
m squared
m
of fencing required.
​(Round to the nearest tenth as​ needed.)

Answer 1

To find the amount of fencing required to enclose a circular garden, we need to calculate the circumference of the circle. The formula for the circumference \( C \) of a circle is given by:

\[
C = 2\pi r
\]

where \( r \) is the radius of the circle.

### Part 1
Given that the radius \( r \) is 21 meters, we can plug it into the formula:

\[
C = 2\pi \times 21
\]

Calculating this gives:

\[
C = 42\pi
\]

So in terms of \(\pi\), the exact amount of fencing required is:

\[
\text{There are } 42\pi \text{ m of fencing required.}
\]

### Part 2
Now, to find the approximate amount of fencing required, we need to calculate \( 42\pi \) using the approximate value of \(\pi\) (about 3.14).

\[
C \approx 42 \times 3.14 = 131.88
\]

Rounding this to the nearest tenth gives:

\[
\text{There are approximately } 131.9 \text{ m of fencing required.}
\]

### Summary
- **Part 1:** \( 42\pi \) m
- **Part 2:** Approximately \( 131.9 \) m