To determine which expression represents the circumference of the circle with a radius of 7 centimeters, let's first recall the formula for the circumference of a circle.
The formula for the circumference [tex]\( C \)[/tex] of a circle is given by:
[tex]\[ C = 2 \pi r \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
Given that the radius [tex]\( r \)[/tex] of the circle is 7 centimeters:
[tex]\[ C = 2 \pi \times 7 \][/tex]
[tex]\[ C = 14 \pi \][/tex]
Now, let's look at the options provided:
A. [tex]\( 2 \times 3.5 \times \pi \)[/tex]
B. [tex]\( 2 \times 14 \times \pi \)[/tex]
C. [tex]\( 72 \times \pi \)[/tex]
D. [tex]\( 14 \times \pi \)[/tex]
- Option A: [tex]\( 2 \times 3.5 \times \pi \)[/tex]
Simplifies to [tex]\( 7 \pi \)[/tex], which is not the correct expression.
- Option B: [tex]\( 2 \times 14 \times \pi \)[/tex]
Simplifies to [tex]\( 28 \pi \)[/tex], which is also not the correct expression.
- Option C: [tex]\( 72 \times \pi \)[/tex]
Clearly, this is not the correct expression as [tex]\( 72 \times \pi \)[/tex] does not correspond with our calculation.
- Option D: [tex]\( 14 \times \pi \)[/tex]
This simplifies directly to what we calculated, [tex]\( 14 \pi \)[/tex].
Hence, the correct expression representing the circumference of the circle is:
D. [tex]\( 14 \times \pi \)[/tex]
