To calculate the total surface area of the cone, we need to use the following formula for the surface area of a cone:

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

where:

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

From the image:

• Radius $r = 2$ meters,
• Slant height $l = 8$ meters.

Now, substituting the values:

$\text{Total Surface Area} = \pi \times 2 \times (2 + 8)$ $= \pi \times 2 \times 10$ $= 20\pi$

Calculating $20\pi$ with $\pi \approx 3.1416$:

$20 \times 3.1416 = 62.8 \, \text{m}^2$

Therefore, the total surface area of the cone is approximately:

$\text{Total Surface Area} = 62.8 \, \text{m}^2$

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

Here are some related questions that expand on this concept:

1. How would the total surface area change if the slant height were different?
2. What is the difference between the lateral surface area and the total surface area of a cone?
3. How can we calculate the slant height if only the height and radius of the cone are given?
4. What is the formula for the volume of a cone, and how is it derived?
5. How does the surface area formula for a cone compare to that for a cylinder?

Tip: Remember, the slant height $l$ in cones is different from the vertical height. It always forms the hypotenuse of the right triangle formed by the radius and vertical height.