The circle has a diameter of $1 \mathrm{~cm}$, as shown. The circumference of the circle is between

(A) $2 \mathrm{~cm}$ and $3 \mathrm{~cm}$

(B) $3 \mathrm{~cm}$ and $4 \mathrm{~cm}$

(C) $4 \mathrm{~cm}$ and $5 \mathrm{~cm}$

(D) $5 \mathrm{~cm}$ and $6 \mathrm{~cm}$

(E) $6 \mathrm{~cm}$ and $8 \mathrm{~cm}$

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-023.jpg?height=295&width=287&top_left_y=1755&top_left_x=1255)
Solution 1

The circumference of a circle, $C$, is given by the formula $C=\pi \times d$, where $d$ is the diameter of the circle.

Since the circle has a diameter of $1 \mathrm{~cm}$, then its circumference is $C=\pi \times 1=\pi \mathrm{cm}$.

Since $\pi$ is approximately 3.14, then the circumference of the circle is between $3 \mathrm{~cm}$ and $4 \mathrm{~cm}$.

## Solution 2

The circumference of a circle, $C$, is given by the formula $C=2 \times \pi \times r$, where $r$ is the radius of the circle.

Since the circle has a diameter of $1 \mathrm{~cm}$, then its radius is $r=\frac{1}{2} \mathrm{~cm}$, and so the circumference is $C=2 \times \pi \times \frac{1}{2}=\pi \mathrm{cm}$.

Since $\pi$ is approximately 3.14, then the circumference of the circle is between $3 \mathrm{~cm}$ and $4 \mathrm{~cm}$.

ANSWER: (B)