Find the missing dimension of a cylinder.
 
V = 787.76cm3, h = 8cm, r = Answer


To find the missing dimension of the cylinder, which is the radius \(r\), we can use the formula for the volume of a cylinder:

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

Given:
- Volume \(V = 787.76 \, \text{cm}^3\)
- Height \(h = 8 \, \text{cm}\)

Now, solve for the radius \(r\):

1. Start by substituting the known values into the formula:

\[
787.76 = \pi r^2 \times 8
\]

2. Solve for \(r^2\):

\[
r^2 = \frac{787.76}{8 \pi}
\]

3. Calculate the right-hand side and then take the square root to find \(r\).

Let me calculate that for you.The radius \( r \) of the cylinder is approximately \( 5.60 \, \text{cm} \).

Would you like more details or have any questions about the process? Here are five related questions for further exploration:

1. How does changing the height affect the volume of a cylinder if the radius is constant?
2. What is the formula for the surface area of a cylinder?
3. How would the volume change if the radius were doubled but the height remained the same?
4. What is the relationship between the radius and the diameter of a cylinder?
5. How can we calculate the height of a cylinder if only the volume and radius are known?

**Tip:** For any cylinder, the volume scales with the square of the radius, so small changes in radius lead to significant changes in volume.

Find the missing dimension of a cylinder. V = 787.76 cm³, h = 8 cm, r = Answer

Learn how to calculate the radius of a cylinder when given the volume (787.76 cm³) and the height (8 cm). This step-by-step guide uses the volume formula for cylinders, V = πr²h, to solve for the radius. Suitable for students in Grades 8-10.

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