**The closed cylinder shown has a total surface area of 1 600 cm2. What is the height of this cylinder if its radius is 8 cm? Use  = 3.142.**




To solve for the height of the cylinder, we can use the formula for the total surface area of a closed cylinder:

\[
\text{Total Surface Area} = 2\pi r(h + r)
\]

Where:
- \( r \) is the radius of the cylinder
- \( h \) is the height of the cylinder
- \( \pi \) is approximately 3.142

Given:
- Total Surface Area \( = 1600 \, \text{cm}^2 \)
- Radius \( r = 8 \, \text{cm} \)
- \( \pi = 3.142 \)

We need to find the height \( h \).

Substitute the given values into the formula:

\[
1600 = 2 \times 3.142 \times 8 \times (h + 8)
\]

Simplify the equation:

\[
1600 = 50.272 \times (h + 8)
\]

Next, divide both sides by 50.272 to isolate \( h + 8 \):

\[
\frac{1600}{50.272} = h + 8
\]

\[
31.83 \approx h + 8
\]

Now, subtract 8 from both sides to solve for \( h \):

\[
h \approx 31.83 - 8
\]

\[
h \approx 23.83 \, \text{cm}
\]

Thus, the height of the cylinder is approximately **23.83 cm**.

Would you like more details or have any questions?

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Here are 8 related questions you might consider:
1. How would the height change if the radius were increased?
2. What is the volume of this cylinder?
3. How does the surface area formula differ for an open cylinder?
4. What happens to the surface area if the height is doubled?
5. Can you derive the formula for the surface area of a cylinder?
6. How would you calculate the lateral surface area alone?
7. What if the surface area were given in square meters instead of square centimeters?
8. How does the surface area change if the radius is halved?

**Tip:** When solving problems involving cylinders, always check if you need the total surface area (including the bases) or just the lateral surface area.

Learn how to find the height of a cylinder given its total surface area of 1600 cm² and radius of 8 cm. Step-by-step solution using the surface area formula. Suitable for Grades 7-9.

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