Question

what is the unit of measurement for volume when using centimeters?
a. cubic centimeters
b. square centimeters
c. centimeters
d. meters
which of the following accurately compares the volume of a cone and cylinder with the same base and height?
a. the cone has twice the volume of the cylinder.
b. the cylinder has one - third the volume of the cone.
c. the cylinder and cone have equal volumes.

Explanation:

• First question: Volume is a three - dimensional measure. The formula for the volume of a solid (like a cube, cylinder, cone etc.) when using centimeters as the linear unit is \(V=\text{length}\times\text{width}\times\text{height}\). So the unit is cubic centimeters (\(cm^{3}\)). Square centimeters (\(cm^{2}\)) is a unit for area (two - dimensional measure), centimeters (\(cm\)) is a unit for length (one - dimensional measure), and meters (\(m\)) is a larger unit for length (not related to the volume when the base unit is centimeters).
• Second question: The volume formula for a cylinder is \(V_{cylinder}=\pi r^{2}h\) (where \(r\) is the radius of the base and \(h\) is the height), and the volume formula for a cone is \(V_{cone}=\frac{1}{3}\pi r^{2}h\). If a cone and a cylinder have the same base (so same \(r\)) and same height (\(h\)), then \(V_{cone}=\frac{1}{3}V_{cylinder}\), which means \(V_{cylinder} = 3V_{cone}\).

Answer:

1. a. cubic centimeters
2. None of the options a, b, c are correct. The correct relationship is that the volume of the cone is one - third of the volume of the cylinder (i.e., \(V_{cone}=\frac{1}{3}V_{cylinder}\)) when they have the same base and height.