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1. What is the circumference and the area of the circle? Round o the nearest tenth. 15 in Work: Circumference= in Area = in²

1. What is the circumference and the area of the circle? Round o the nearest tenth. 15 in Work: Circumference= in Area = in²

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter62: Volumes Of Prisms And Cylinders
Section: Chapter Questions
Problem 38A: A copper casting is in the shape of a prism with an equilateral triangle base. The length of each...
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### Determining the Circumference and Area of a Circle **Problem 21:** What is the circumference and the area of the circle? Round the calculations to the nearest tenth. **Given Information:** - The radius of the circle is 15 inches. **Diagram:** - A circle with a labeled radius of 15 inches is depicted on the left-hand side. **Calculation Steps and Solution:** --- *Work:* (To be filled out by the student) **Formulas:** - Circumference of a circle: \( C = 2\pi r \) - Area of a circle: \( A = \pi r^2 \) Where: - \( r \) is the radius of the circle - \( \pi \) (pi) is approximately 3.14159 1. **Circumference Calculation:** \( C = 2\pi r \) Plug in the radius \( r = 15 \) inches: \( C = 2 \cdot 3.14159 \cdot 15 \) \( C \approx 94.2 \) inches (rounded to the nearest tenth) 2. **Area Calculation:** \( A = \pi r^2 \) Plug in the radius \( r = 15 \) inches: \( A = 3.14159 \cdot (15)^2 \) \( A \approx 706.9 \) square inches (rounded to the nearest tenth) --- **Result:** - **Circumference:** Approximately 94.2 inches - **Area:** Approximately 706.9 square inches Completion of this practice will help reinforce the understanding of calculating basic geometric properties of circles.
Transcribed Image Text:### Determining the Circumference and Area of a Circle **Problem 21:** What is the circumference and the area of the circle? Round the calculations to the nearest tenth. **Given Information:** - The radius of the circle is 15 inches. **Diagram:** - A circle with a labeled radius of 15 inches is depicted on the left-hand side. **Calculation Steps and Solution:** --- *Work:* (To be filled out by the student) **Formulas:** - Circumference of a circle: \( C = 2\pi r \) - Area of a circle: \( A = \pi r^2 \) Where: - \( r \) is the radius of the circle - \( \pi \) (pi) is approximately 3.14159 1. **Circumference Calculation:** \( C = 2\pi r \) Plug in the radius \( r = 15 \) inches: \( C = 2 \cdot 3.14159 \cdot 15 \) \( C \approx 94.2 \) inches (rounded to the nearest tenth) 2. **Area Calculation:** \( A = \pi r^2 \) Plug in the radius \( r = 15 \) inches: \( A = 3.14159 \cdot (15)^2 \) \( A \approx 706.9 \) square inches (rounded to the nearest tenth) --- **Result:** - **Circumference:** Approximately 94.2 inches - **Area:** Approximately 706.9 square inches Completion of this practice will help reinforce the understanding of calculating basic geometric properties of circles.
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