Calculate the height of a closed cylinder whose radius is 7 cm and surface area is 924cm. (Take pie=22/7)

To find the height of a closed cylinder given the radius and the surface area, we can use the formula for the surface area of a cylinder:

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

Where:
- \(\pi\) is approximately \(\frac{22}{7}\)
- \(r\) is the radius of the cylinder
- \(h\) is the height of the cylinder

Given:
- \(r = 7 \, \text{cm}\)
- Surface Area = \(924 \, \text{cm}^2\)

Substituting the values into the formula:

\[
924 = 2 \times \frac{22}{7} \times 7 \times (h + 7)
\]

Simplify:

\[
924 = 2 \times 22 \times (h + 7)
\]

\[
924 = 44(h + 7)
\]

Now, divide both sides by 44:

\[
\frac{924}{44} = h + 7
\]

\[
21 = h + 7
\]

Finally, subtract 7 from both sides to find the height:

\[
h = 21 - 7 = 14 \, \text{cm}
\]

So, the height of the cylinder is **14 cm**.

Would you like further details or explanations? 

Here are some related questions you might find interesting:
1. What would be the height if the surface area was 1848 cm²?
2. How does the surface area change if the radius is doubled?
3. What is the volume of this cylinder?
4. If the height were doubled, how would that affect the surface area?
5. What would happen to the surface area if the height and radius were both doubled?

**Tip:** Always double-check whether the problem refers to the total surface area (including both bases) or just the lateral surface area, as this affects the formula used.

Calculate the height of a closed cylinder whose radius is 7 cm and surface area is 924 cm². (Take π = 22/7)

Discover how to calculate the height of a closed cylinder with a radius of 7 cm and a surface area of 924 cm² using the formula for the surface area of a cylinder. This problem involves key geometric concepts and algebraic manipulation, making it suitable for students in Grades 8-10.

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