Question

complete the table by finding the radius, circumference, and area. Round to the nearest hundredths.
Radius Circumference Area
17 in. ? in. ?
?cm 53.38 cm ?
? ft. ? ft. 1962.5 ft

Answer 1

To complete the table, we'll use the following formulas:

1. **Circumference (C)** = \( 2 \pi r \)
2. **Area (A)** = \( \pi r^2 \)

Let's solve for each missing value one by one.

### 1. For the first row with a radius of 17 inches:

- Circumference:
\[ C = 2 \pi r = 2 \pi (17) \approx 106.81 \, \text{in.} \]
- Area:
\[ A = \pi r^2 = \pi (17^2) \approx 907.57 \, \text{in}^2 \]

### 2. For the second row with a circumference of 53.38 cm:

- Radius:
First, rearranging the circumference formula to find \( r \):
\[ r = \frac{C}{2 \pi} = \frac{53.38}{2 \pi} \approx \frac{53.38}{6.2832} \approx 8.49 \, \text{cm} \]
- Area:
\[ A = \pi r^2 \approx \pi (8.49^2) \approx \pi (72.5) \approx 228.96 \, \text{cm}^2 \]

### 3. For the third row with an area of 1962.5 ft²:

- Radius:
Using the area formula rearranged to find \( r \):
\[ r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{1962.5}{\pi}} \approx \sqrt{\frac{1962.5}{3.14159}} \approx \sqrt{624.56} \approx 24.98 \, \text{ft} \]
- Circumference:
\[ C = 2 \pi r \approx 2 \pi (24.98) \approx 156.56 \, \text{ft} \]

### Completed Table
Now we can fill in the completed table with the values calculated:

| Radius | Circumference | Area |
|------------|---------------|------------|
| 17 in. | 106.81 in. | 907.57 in² |
| 8.49 cm | 53.38 cm | 228.96 cm² |
| 24.98 ft | 156.56 ft | 1962.5 ft² |

Make sure to round the final answers as required, though I've used the standard rounding in calculations. Each number is rounded to the nearest hundredth as specified.