https://file.aiquickdraw.com/mathbot/file/17261575038152jdc9u5u.jpg

The image presents a right cylinder with a height of \( h = 8 \, \text{m} \) and a radius of \( r = 2.5 \, \text{m} \). The problems are to find:

1. **The total surface area of the cylinder**, rounded to 2 decimal places.
2. **The volume of the cylinder**, also rounded to 2 decimal places.

### 1. Total Surface Area of the Cylinder

The formula for the total surface area \( A \) of a cylinder is:

\[
A = 2\pi r^2 + 2\pi rh
\]

Where:
- \( r \) is the radius,
- \( h \) is the height.

### 2. Volume of the Cylinder

The formula for the volume \( V \) of a cylinder is:

\[
V = \pi r^2 h
\]

Let me calculate both.Here are the results:

1. **Total Surface Area**: \( 164.93 \, \text{m}^2 \) (rounded to 2 decimal places).
2. **Volume**: \( 157.08 \, \text{m}^3 \) (rounded to 2 decimal places).

Do you need further details or have any questions?

Here are five related questions you might find helpful:
1. How does changing the radius affect the surface area of a cylinder?
2. What happens to the volume if the height is doubled?
3. Can you derive the lateral surface area of a cylinder using only its height and radius?
4. How is the volume of a cylinder related to the volume of a cone with the same base and height?
5. What real-world objects resemble the shape of a cylinder, and how are their surface areas or volumes calculated?

**Tip**: When calculating surface area, remember to account for both the lateral area and the two circular bases!

Find the total surface area and volume of a cylinder with a height of 8 meters and a radius of 2.5 meters. Round to 2 decimal places.

Learn how to calculate the total surface area and volume of a cylinder with a height of 8 meters and a radius of 2.5 meters. This step-by-step solution includes essential geometry concepts and key formulas for cylindrical shapes, ideal for students in Grades 8-10.

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