To calculate the cross-sectional area of the cylinder, we are dealing with the circular face of the cylinder. The formula for the area $A$ of a circle is:

$A = \pi r^2$

where:

• $r$ is the radius of the circle,
• $\pi$ is approximately 3.14159.

From the image, the diameter of the cylinder is given as 46 cm. The radius is half the diameter:

$r = \frac{46}{2} = 23 \, \text{cm}$

Now, we substitute the radius into the formula:

$A = \pi \times 23^2 = \pi \times 529$

$A \approx 3.14159 \times 529 = 1662.76 \, \text{cm}^2$

Thus, the cross-sectional area of the cylinder is approximately 1662.8 cm² (to 1 decimal place).

Would you like further details on the solution or have any questions?

Here are 5 related questions to explore further:

1. How would the cross-sectional area change if the diameter were doubled?
2. What is the formula to calculate the volume of the entire cylinder if its height were given?
3. How does the cross-sectional area of a cylinder compare to its lateral surface area?
4. How would you calculate the surface area of a hollow cylinder with a given thickness?
5. What are the applications of cross-sectional area in physics and engineering?

Tip: When solving problems involving circles, always ensure you use the correct radius, as it's easy to mistakenly use the diameter in formulas that require the radius.