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. 
Remaining Attempts : 3

Answer 1

To find the volume of the pyramid, we need to use the formulas for the volumes of a cube and a pyramid, and the information given.

1. Volume of a Cube: The volume \( V \) of a cube is given by the formula: \[ V = a \cdot h \] where \( a \) is the base area and \( h \) is the height.

   We are given that the volume of the cube is 195 cm³. Thus, we can express this as: \[ a \cdot h = 195 \quad \text{(Equation 1)} \]

2. Volume of a Pyramid: The volume \( V_{\text{pyramid}} \) of a pyramid with a square base is given by the formula: \[ V_{\text{pyramid}} = \frac{1}{3} \cdot a \cdot h \]

3. Substituting from Equation 1 into the Pyramid's Volume Formula: Since \( a \cdot h = 195 \), we substitute \( 195 \) into the formula for the volume of the pyramid: \[ V_{\text{pyramid}} = \frac{1}{3} \cdot 195 \] \[ V_{\text{pyramid}} = \frac{195}{3} = 65 \]

Thus, the volume of the pyramid is 65 cubic centimeters.