Answered

IDNLearn.com offers a user-friendly platform for finding and sharing knowledge. Ask any question and receive timely, accurate responses from our dedicated community of experts.

If [tex]\( r \)[/tex] is the radius of a circle and [tex]\( d \)[/tex] is its diameter, which of the following is an equivalent formula for the circumference [tex]\( C = 2 \pi r \)[/tex]?

A. [tex]\( C = 2 \pi d \)[/tex]
B. [tex]\( C = \pi r d \)[/tex]
C. [tex]\( C = \pi d^2 \)[/tex]
D. [tex]\( C = \pi d \)[/tex]

Sagot :

GinnyAnsweridn
To determine the equivalent formula for the circumference [tex]\(C\)[/tex] in terms of the diameter [tex]\(d\)[/tex], we start with the known formula for the circumference of a circle:

[tex]\[ C = 2 \pi r \][/tex]

where [tex]\(r\)[/tex] is the radius of the circle. We also know the relationship between the diameter [tex]\(d\)[/tex] and the radius [tex]\(r\)[/tex] of a circle:
[tex]\[ d = 2r \][/tex]

Let's substitute [tex]\(r\)[/tex] in the circumference formula using this relationship:

[tex]\[ C = 2 \pi r \][/tex]
[tex]\[ r = \frac{d}{2} \][/tex]

Substitute [tex]\(\frac{d}{2}\)[/tex] for [tex]\(r\)[/tex] in the formula for circumference:

[tex]\[ C = 2 \pi \left( \frac{d}{2} \right) \][/tex]

Now, simplify the equation:

[tex]\[ C = 2 \pi \cdot \frac{d}{2} \][/tex]
[tex]\[ C = \pi d \][/tex]

Therefore, the equivalent formula for the circumference [tex]\(C\)[/tex] in terms of the diameter [tex]\(d\)[/tex] is:

[tex]\[ C = \pi d \][/tex]

Looking at the given choices, the correct answer is:

D. [tex]\(C = \pi d\)[/tex]
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.