Question

if a cone is one - third the volume of a cylinder with the same base and height, what is the formula for its volume?
a. ( v=\frac{1}{2}pi r^{2}h )
b. ( v=\frac{1}{4}pi r^{2}h )
c. ( v=pi rh )
d. ( v=\frac{1}{3}pi r^{2}h )
which unit is used to measure the volume of a cone?
a. linear units
b. cubic units
c. square units
d. none of the answers

Explanation:

First Question:

Step1: Recall the volume formula of a cylinder

The volume formula of a cylinder is \(V = \pi r^{2}h\).

Step2: Use the given relationship between cone and cylinder volume

Since the cone's volume is one - third of the cylinder's volume (with the same base \(r\) and height \(h\)), we multiply the cylinder's volume formula by \(\frac{1}{3}\). So the cone's volume formula is \(V=\frac{1}{3}\pi r^{2}h\).

Second Question:

Step1: Recall the nature of volume measurement

Volume is a three - dimensional measure. Linear units (\(m\), \(cm\) etc.) measure one - dimensional length, square units (\(m^{2}\), \(cm^{2}\) etc.) measure two - dimensional area. Cubic units (\(m^{3}\), \(cm^{3}\) etc.) measure three - dimensional volume.

Answer:

For the first question: d. \(V = \frac{1}{3}\pi r^{2}h\)
For the second question: b. cubic units