9. A circular pond has a radius of 6 feet. If lights are placed about every 4 feet along the edge, how many lights will be required? Round to the nearest whole number. You will need Put the number in the first blank, the label in the second blank.

To determine how many lights are required around the circular pond, we need to follow these steps: 1. **Calculate the circumference of the pond**: The formula for the circumference \( C \) of a circle is given by: \[ C = 2 \pi r \] where \( r \) is the radius of the circle. 2. **Substitute the known value**: In this case, the radius \( r \) is 6 feet. 3. **Calculate the number of lights**: Since lights are placed every 4 feet along the edge, we will divide the circumference by the distance between the lights to find the total number of lights needed. 4. **Round to the nearest whole number**: Since we cannot have a fraction of a light, we will round the result to the nearest whole number. Let's perform the calculations step by step. ### Step 1: Calculate the circumference Using the formula: \[ C = 2 \pi r \] Substituting \( r = 6 \): \[ C = 2 \pi \times 6 \] ### Step 2: Calculate the number of lights Now, we will divide the circumference by the distance between the lights (4 feet): \[ \text{Number of lights} = \frac{C}{4} \] Now, let's calculate these values. Calculate the value by following steps: - step0: Calculate: \(2\pi \times 6\) - step1: Multiply the terms: \(12\pi \) Calculate or simplify the expression \( (2 * \pi * 6) / 4 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\left(2\pi \times 6\right)}{4}\) - step1: Remove the parentheses: \(\frac{2\pi \times 6}{4}\) - step2: Multiply the terms: \(\frac{12\pi }{4}\) - step3: Reduce the fraction: \(3\pi \) ### Step 1: Calculate the circumference The circumference \( C \) of the pond is: \[ C = 2 \pi \times 6 \approx 37.70 \text{ feet} \] ### Step 2: Calculate the number of lights Now, we divide the circumference by the distance between the lights (4 feet): \[ \text{Number of lights} = \frac{C}{4} \approx \frac{37.70}{4} \approx 9.42 \] ### Step 3: Round to the nearest whole number Rounding \( 9.42 \) to the nearest whole number gives us \( 9 \). ### Final Answer - Number of lights required: **9** - Label: **lights** So, the answer is: - **9** lights