To calculate the total surface area of a cone, we use the formula:

$\text{Total Surface Area} = \pi r (r + l)$

where:

• $r$ is the radius of the base,
• $l$ is the slant height of the cone.

From the diagram:

• The radius $r = 3 \, \text{cm}$,
• The slant height $l = 6 \, \text{cm}$.

Now, plug these values into the formula:

$\text{Total Surface Area} = \pi \times 3 \times (3 + 6) = \pi \times 3 \times 9 = 27\pi$

Calculating this:

$\text{Total Surface Area} \approx 27 \times 3.1416 = 84.8 \, \text{cm}^2$

So, the total surface area is approximately $84.8 \, \text{cm}^2$.

Would you like further details, or do you have any questions?

Related Questions

1. How do you find the slant height if only the height and radius are given?
2. What is the difference between lateral surface area and total surface area of a cone?
3. How does the surface area formula change for a cylinder?
4. How can you derive the surface area formula for a cone?
5. What is the surface area of a cone if the radius and slant height are doubled?

Tip: Remember, the slant height is crucial for calculating the cone's surface area accurately, especially when the cone's height is given instead of the slant height.