A square-based pyramid has height h and base area a. A cube has the same base area and the same height. If the cube has a volume of 195 cubic centimeters, what is the volume of the pyramid?(1 point)

Question

The pyramid has a volume of
cubic centimeters. 

Answer 1

To find the volume of the square-based pyramid, we can use the formulas for volume.

1. Volume of the cube: The volume \( V \) of a cube is given by

   \[ V = \text{base area} \times \text{height} \]

   Since the cube has the same base area \( a \) and height \( h \), the volume of the cube is also:

   \[ V_{\text{cube}} = a \times h \]

   We know from the problem that the volume of the cube is 195 cubic centimeters, so:

   \[ a \times h = 195 \quad (1) \]

2. Volume of the pyramid: The volume \( V \) of a pyramid is given by

   \[ V = \frac{1}{3} \times \text{base area} \times \text{height} \]

   For our pyramid, this becomes:

   \[ V_{\text{pyramid}} = \frac{1}{3} a \times h \]

3. Relate the volume of the pyramid to the volume of the cube: From equation (1), we know that \( a \times h = 195 \). Substituting this into the volume formula for the pyramid, we get:

   \[ V_{\text{pyramid}} = \frac{1}{3} \times 195 \]

   Now, we calculate that:

   \[ V_{\text{pyramid}} = \frac{195}{3} = 65 \]

Thus, the volume of the pyramid is

\[ \boxed{65} \text{ cubic centimeters.} \]