Unit 10 Circles Homework 1 is an important assignment for students studying circles in mathematics. This article aims to provide a detailed answer key to help students understand the concepts and solve the problems effectively. The comprehensive solutions presented here will guide students through the various exercise questions, allowing them to check their answers and improve their understanding of circle-related concepts.
Unit 10 Circles Homework 1: Detailed Answer Key
- Question: Find the circumference of a circle with a radius of 7 cm.
Solution: The formula for finding the circumference of a circle is C = 2πr, where r represents the radius of the circle. Substituting the given radius value, we get C = 2π(7) = 14π cm. Therefore, the circumference of the circle is 14π cm.
- Question: Determine the area of a circle with a diameter of 10 units.
Solution: The formula for finding the area of a circle is A = πr², where r represents the radius of the circle. As the diameter is double the radius, we can find the radius by dividing the diameter by 2. In this case, the radius is 10/2 = 5 units. Substituting the value of the radius, we get A = π(5)² = 25π square units. Hence, the area of the circle is 25π square units.
- Question: A circular field has a circumference of 36 meters. Find the radius of the field.
Solution: The formula for finding the circumference of a circle is C = 2πr. Rearranging the formula to solve for the radius, we have r = C/(2π). Substituting the given circumference value, we get r = 36/(2π) = 18/π meters. Therefore, the radius of the field is 18/π meters.
Unit 10 Circles Homework 1 can be challenging, but with the detailed answer key provided above, students can easily comprehend the concepts related to circles and solve the problems accurately. By understanding the formulas and techniques used in finding the circumference and area of circles, students will not only excel in their homework but also develop a strong foundation in geometry. Practice and repetition are key to mastering these concepts, so students are encouraged to attempt similar exercises to reinforce their knowledge.