Thank you for visiting Which statements about the clock are accurate Choose three correct answers A The circumference of the clock is approximately 62 8 inches B The length. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Let's analyze the problem step-by-step.
1. We assume that the clock has a radius of [tex]$10$[/tex] inches.
2. The circumference [tex]$C$[/tex] of a circle is calculated using the formula
[tex]$$
C = 2 \pi r.
$$[/tex]
Substituting the radius [tex]$r = 10$[/tex] inches, we have
[tex]$$
C = 2 \pi (10) \approx 62.8 \text{ inches}.
$$[/tex]
3. The clock face is divided into [tex]$12$[/tex] equal sections (one for each hour). Therefore, the angle between any two adjacent hour marks is
[tex]$$
\frac{360^\circ}{12} = 30^\circ.
$$[/tex]
4. The length of the minor arc between any two consecutive hour marks (for example, between 6 and 7) can be calculated by taking the fraction of the circumference corresponding to [tex]$30^\circ$[/tex]. This is given by
[tex]$$
\text{Arc Length} = \left(\frac{30}{360}\right) \times C = \frac{1}{12} \times 62.8 \approx 5.2 \text{ inches}.
$$[/tex]
5. In summary, the following statements are accurate:
- The clock has a radius of [tex]$10$[/tex] inches.
- The circumference of the clock is approximately [tex]$62.8$[/tex] inches.
- The length of the minor arc between 6 and 7 is approximately [tex]$5.2$[/tex] inches.
Thus, these three statements about the clock are correct.
1. We assume that the clock has a radius of [tex]$10$[/tex] inches.
2. The circumference [tex]$C$[/tex] of a circle is calculated using the formula
[tex]$$
C = 2 \pi r.
$$[/tex]
Substituting the radius [tex]$r = 10$[/tex] inches, we have
[tex]$$
C = 2 \pi (10) \approx 62.8 \text{ inches}.
$$[/tex]
3. The clock face is divided into [tex]$12$[/tex] equal sections (one for each hour). Therefore, the angle between any two adjacent hour marks is
[tex]$$
\frac{360^\circ}{12} = 30^\circ.
$$[/tex]
4. The length of the minor arc between any two consecutive hour marks (for example, between 6 and 7) can be calculated by taking the fraction of the circumference corresponding to [tex]$30^\circ$[/tex]. This is given by
[tex]$$
\text{Arc Length} = \left(\frac{30}{360}\right) \times C = \frac{1}{12} \times 62.8 \approx 5.2 \text{ inches}.
$$[/tex]
5. In summary, the following statements are accurate:
- The clock has a radius of [tex]$10$[/tex] inches.
- The circumference of the clock is approximately [tex]$62.8$[/tex] inches.
- The length of the minor arc between 6 and 7 is approximately [tex]$5.2$[/tex] inches.
Thus, these three statements about the clock are correct.
Thank you for reading the article Which statements about the clock are accurate Choose three correct answers A The circumference of the clock is approximately 62 8 inches B The length. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
