To find the circumference of the bottom of the teacup, we can use the formula for the circumference of a circle:

$C = 2\pi r$

Where:

• $C$ is the circumference,
• $r$ is the radius of the circle, and
• $\pi \approx 3.1416$.

Given that the radius of the teacup is 4 centimeters, we can substitute this value into the formula:

$C = 2\pi(4) \approx 2 \times 3.1416 \times 4 \approx 25.132 \, \text{cm}$

Rounding to the nearest tenth:

$C \approx 25.1 \, \text{cm}$

Thus, the circumference of the bottom of the teacup is approximately 25.1 centimeters.

Would you like further explanation or have any questions on the topic? Here are some related questions:

1. How would the circumference change if the radius of the teacup were doubled?
2. What is the area of the bottom of the teacup if the radius is 4 cm?
3. How can you find the diameter of a circle given its circumference?
4. How does the formula for circumference change for a circle with a different unit of measurement?
5. Can you calculate the circumference of a circle if you only know the diameter?

Tip: Remember, when working with circles, the relationship between radius, diameter, and circumference is key!