Write true or false.
The largest possible right circularr cone is cut out of a cube of edge r cm. the volume of the cone is `(1)/(12)pir^(3)` (T/F).

Answer

To determine whether the statement is true or false, we need to calculate the volume of the largest right circular cone that can be cut from a cube of edge length \( r \) cm.

### Step-by-Step Solution

1. **Understanding the Geometry**:
- A cube has all edges of equal length. In this case, the edge length is \( r \) cm.
- The largest right circular cone that can be inscribed in the cube will have its base on one face of the cube and its vertex at the opposite face.

2. **Identifying the Dimensions of the Cone**:
- The diameter of the base of the cone will be equal to the edge length of the cube, which is \( r \) cm.
- Therefore, the radius \( R \) of the cone's base is:
\[ R = \frac{r}{2} \]
- The height \( h \) of the cone will be equal to the edge length of the cube, which is \( r \) cm.

3. **Using the Formula for the Volume of a Cone**:
- The volume \( V \) of a cone is given by the formula:
\[ V = \frac{1}{3} \pi R^2 h \]
- Substituting the values of \( R \) and \( h \):
\[ V = \frac{1}{3} \pi \left(\frac{r}{2}\right)^2 r \]

4. **Calculating the Volume**:
- First, calculate \( R^2 \):
\[ R^2 = \left(\frac{r}{2}\right)^2 = \frac{r^2}{4} \]
- Now substitute \( R^2 \) into the volume formula:
\[ V = \frac{1}{3} \pi \left(\frac{r^2}{4}\right) r = \frac{1}{3} \pi \frac{r^3}{4} \]
- Simplifying further:
\[ V = \frac{\pi r^3}{12} \]

5. **Conclusion**:
- The calculated volume of the cone is:
\[ V = \frac{1}{12} \pi r^3 \]
- This matches the statement given in the question.

Thus, the statement is **True**.