https://file.aiquickdraw.com/mathbot/file/1727292053155fkl0fhe5.jpg

The image provides a formula for the surface area of a cone, which is:

\[
\text{Surface Area} = \pi r \ell + \pi r^2
\]

Where:
- \( r \) is the radius of the base of the cone.
- \( \ell \) is the slant height of the cone.

From the image:
- The radius \( r = 9 \, \text{cm} \).
- The height \( h = 21 \, \text{cm} \).

First, we need to calculate the slant height \( \ell \). Using the Pythagorean theorem for the right triangle formed by the height, radius, and slant height, we get:

\[
\ell = \sqrt{h^2 + r^2}
\]

Now, let's compute the slant height \( \ell \) and the surface area.The slant height \( \ell \) of the cone is approximately \( 22.85 \, \text{cm} \).

Now, applying the surface area formula:
\[
\text{Surface Area} = \pi r \ell + \pi r^2
\]
Substituting the values:
\[
\text{Surface Area} = \pi (9)(22.85) + \pi (9^2)
\]
\[
\text{Surface Area} = \pi \times 205.62 + \pi \times 81 = \pi \times 286.62
\]

Therefore, the surface area is approximately:
\[
286.62 \pi \, \text{cm}^2
\]

Let me know if you have any questions or would like further details! Here are some related questions for you:

1. How does the Pythagorean theorem help find the slant height of a cone?
2. What is the difference between the lateral surface area and the total surface area of a cone?
3. How would the surface area formula change if the cone had a different shape (like a truncated cone)?
4. Can you derive the surface area of a cone without using the formula provided?
5. How would the surface area be affected if both the height and radius were doubled?

**Tip:** Always double-check whether you're calculating the total surface area (including the base) or just the lateral surface area when solving cone problems!

Find the surface area of the cone below. Leave your answer in terms of π.

Learn how to calculate the surface area of a cone with a radius of 9 cm and a height of 21 cm. Using the surface area formula and Pythagorean theorem, find the slant height and solve the surface area step-by-step. Perfect for students in Grades 9-10.

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