4. What is the circumference of a circle with a radius of 5 inches? 5. What is the diameter of a circle with a circumference of 10.99 feet?

Question

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$2\pi \times 5$$
- step1: Multiply the terms:
  $$10\pi $$
Solve the equation $$ C = \pi * d $$.
Solve the equation by following steps:
- step0: Solve for $$d$$:
  $$C=\pi d$$
- step1: Swap the sides:
  $$\pi d=C$$
- step2: Divide both sides:
  $$\frac{\pi d}{\pi }=\frac{C}{\pi }$$
- step3: Divide the numbers:
  $$d=\frac{C}{\pi }$$
Let's solve each part of your question step by step.

### 1. Circumference of a Circle with a Radius of 5 Inches

The formula for the circumference $$ C $$ of a circle is given by:

$$
C = 2 \pi r
$$

where $$ r $$ is the radius. In this case, the radius $$ r = 5 $$ inches.

Substituting the value into the formula:

$$
C = 2 \pi (5) = 10 \pi
$$

Calculating the numerical value:

$$
C \approx 31.415927 \text{ inches}
$$

So, the circumference of the circle is approximately **31.42 inches**.

### 2. Diameter of a Circle with a Circumference of 10.99 Feet

The relationship between the circumference $$ C $$ and the diameter $$ d $$ of a circle is given by:

$$
C = \pi d
$$

To find the diameter, we can rearrange this formula:

$$
d = \frac{C}{\pi}
$$

Substituting the given circumference $$ C = 10.99 $$ feet:

$$
d = \frac{10.99}{\pi}
$$

Calculating this gives us the diameter. Let's compute that value:

$$
d \approx \frac{10.99}{3.14159} \approx 3.5 \text{ feet}
$$

So, the diameter of the circle is approximately **3.5 feet**.

### Summary of Results
- The circumference of the circle with a radius of 5 inches is approximately **31.42 inches**.
- The diameter of the circle with a circumference of 10.99 feet is approximately **3.5 feet**.
- The circumference of a circle with a 5-inch radius is approximately **31.42 inches**. - The diameter of a circle with a circumference of 10.99 feet is approximately **3.5 feet**.

4. What is the circumference of a circle with a radius of 5 inches? 5. What is the diameter of a circle with a circumference of 10.99 feet?

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