Question

a circular pond has a radius of 8 3/4 feet. What is the approximate circumference, in feet. of the pound (use 22/7 for PI)

Answer 1

To calculate the circumference of a circular pond, you can use the formula:

\[
\text{Circumference} = 2 \times \pi \times r
\]

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

Given that the radius is \( 8 \frac{3}{4} \) feet, we first convert this mixed number into an improper fraction:

\[
8 \frac{3}{4} = 8 + \frac{3}{4} = \frac{32}{4} + \frac{3}{4} = \frac{35}{4} \text{ feet}
\]

Now we use \( \pi \) as \( \frac{22}{7} \). Plugging in the radius into the circumference formula, we have:

\[
\text{Circumference} = 2 \times \frac{22}{7} \times \frac{35}{4}
\]

Now we can simplify this step by step:

1. Multiply \( 2 \) and \( \frac{35}{4} \):

\[
2 \times \frac{35}{4} = \frac{70}{4} = \frac{35}{2}
\]

2. Now, substitute it back into the circumference formula:

\[
\text{Circumference} = \frac{22}{7} \times \frac{35}{2}
\]

3. Multiply the fractions:

\[
= \frac{22 \times 35}{7 \times 2} = \frac{770}{14}
\]

4. Now simplify \( \frac{770}{14} \):

\[
= \frac{385}{7}
\]

5. Finally, divide \( 385 \) by \( 7 \):

\[
385 \div 7 = 55
\]

Thus, the approximate circumference of the pond is **55 feet**.