What is the volume of a cylinder with base radius
\[4\] and height
\[7\]?

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

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

where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.

Given:
- \( r = 4 \)
- \( h = 7 \)

Substitute these values into the formula:

\[
V = \pi (4)^2 (7)
\]

\[
V = \pi \times 16 \times 7
\]

\[
V = 112\pi \text{ cubic units}
\]

So, the volume of the cylinder is \( 112\pi \) cubic units, or approximately \( 351.86 \) cubic units when \( \pi \) is approximated as \( 3.14159 \).

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. How would the volume change if the height of the cylinder were doubled?
2. What is the surface area of the cylinder with the given dimensions?
3. How would the volume change if the radius were halved?
4. What is the relationship between the volume of a cylinder and its height?
5. How does the volume of a cylinder compare to that of a cone with the same base and height?

**Tip:** Remember that doubling the radius of a cylinder quadruples its volume, as the radius is squared in the volume formula.

Learn how to calculate the volume of a cylinder with a radius of 4 units and a height of 7 units using the formula V = π r^2 h. Get a detailed step-by-step solution with the volume calculated as 112π cubic units or approximately 351.86 cubic units.

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