The volume of a cylinder is the base (B) times the length of its height ($h$). Which of the following is the formula for the volume of a cylinder?
A. $V=\frac{1}{2} B h$
B. $V=-B h$
C. $V=2 B w$
D. $V=B h$
Answer (1)
The problem defines the volume of a cylinder as the product of its base and height.
We analyze each option to find the formula that matches this definition.
Option D, V = B h , correctly represents the volume of a cylinder.
The correct formula for the volume of a cylinder is: V = B h .
Explanation
Problem Analysis The problem states that the volume of a cylinder is the base (B) times the height (h). We need to identify the correct formula from the given options.
Evaluate Options Let's examine each option:
Option A: V = 2 1 B h . This formula includes a factor of 2 1 , which is not part of the standard volume formula for a cylinder.
Option B: V = − B h . This formula includes a negative sign, indicating a negative volume, which is not physically possible.
Option C: V = 2 Bw . This formula uses 'w' instead of 'h' for the height and includes a factor of 2, which is incorrect.
Option D: V = B h . This formula matches the statement that the volume is the base times the height.
Identify Correct Formula Therefore, the correct formula for the volume of a cylinder is V = B h .
Additional Information The formula for the volume of a cylinder is the area of its base multiplied by its height. The base of a cylinder is a circle, so its area is given by B = π r 2 , where r is the radius of the base. Therefore, the volume of a cylinder can also be expressed as V = π r 2 h .
Examples
Understanding the volume of a cylinder is useful in many real-world scenarios. For example, when calculating how much liquid a cylindrical container can hold, such as a can of soup or a water tank. If you know the base area and the height, you can easily find the volume using the formula V = B h . This is also applicable in construction, where you might need to calculate the volume of cylindrical pillars or pipes.
