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A gardener makes a new circular flower bed. The bed is twelve feet in diameter. Calculate the circumference and the area of the circular flower bed. circumference \( =12 \) feet, area \( =12 \pi \) square feet circumference \( =12 \pi \) feet, area \( =144 \pi \) square feet circumference \( =12 \pi \) feet, area \( =36 \pi \) square feet circumference \( =6 \pi \) feet, area \( =36 \pi \) square feet

Ask by Edwards Bernard. in the United States
Jan 25,2025

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Tutor-Verified Answer

Answer

Circumference: \(12\pi\) feet Area: \(36\pi\) square feet

Solution

To determine the correct circumference and area of the circular flower bed with a diameter of 12 feet, let's perform the calculations step by step. ### 1. Circumference The formula for the circumference \( C \) of a circle is: \[ C = \pi \times \text{diameter} \] Given: - Diameter \( d = 12 \) feet Calculating: \[ C = \pi \times 12 = 12\pi \text{ feet} \] ### 2. Area The formula for the area \( A \) of a circle is: \[ A = \pi \times r^2 \] First, determine the radius \( r \): \[ r = \frac{\text{diameter}}{2} = \frac{12}{2} = 6 \text{ feet} \] Calculating: \[ A = \pi \times 6^2 = \pi \times 36 = 36\pi \text{ square feet} \] ### Conclusion Based on the calculations: - **Circumference:** \( 12\pi \) feet - **Area:** \( 36\pi \) square feet **Correct Option:** **circumference \( =12 \pi \) feet, area \( =36 \pi \) square feet**

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Beyond the Answer

Did you know that the formula for the circumference of a circle is \( C = \pi d \), where \( d \) is the diameter? So, for your flower bed with a diameter of 12 feet, the circumference would be \( C = \pi \times 12 = 12\pi \) feet. As for the area, you can use \( A = \pi r^2 \), with \( r \) being the radius (6 feet). This gives us \( A = \pi \times 6^2 = 36\pi \) square feet! If you're looking to create a perfect circular flower bed, remember to measure the diameter and use that to find your radius. Setting up a string around a stake in the center can help ensure your circle is even. A common mistake is to forget that the radius is half the diameter, leading to errors in area calculations. So keep those measurements in mind for a blooming success!

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