Question

Three cones with the same size base and height as a cylinder is filled with water. The water in the cones are then transferred to the cylinder.

What is the relationship between the volume of each cone and cylinder?

When given a cone with the same base and height as a cylinder, the volume of the cylinder is *blank 1* times the volume of the cone.

Another way to think about this is, the volume of the cone is *blank 2* the volume of the cylinder with the same base and height

Options for both blanks

A 1/4
B 3
C 1/2
D 4
E 1/3
F 2

Answer 1

The volume of a cone is given by the formula:

\[
V_{\text{cone}} = \frac{1}{3} \pi r^2 h
\]

where \( r \) is the radius of the base and \( h \) is the height of the cone.

The volume of a cylinder is given by the formula:

\[
V_{\text{cylinder}} = \pi r^2 h
\]

To compare the volumes, we can find the ratio of the cylinder's volume to the cone's volume.

\[
\text{Volume ratio} = \frac{V_{\text{cylinder}}}{V_{\text{cone}}} = \frac{\pi r^2 h}{\frac{1}{3} \pi r^2 h} = 3
\]

This tells us that the volume of the cylinder is 3 times the volume of the cone.

So to fill in the blanks:

1. The volume of the cylinder is **3** times the volume of the cone (blank 1 = B).
2. The volume of the cone is **1/3** the volume of the cylinder (blank 2 = E).

Thus, the answers are:
- blank 1: B (3)
- blank 2: E (1/3)