What is the volume of a compound solid made of a cube and a pyramid?

The volume of a compound solid made of a cube and a pyramid is the sum of their individual volumes.

To find the volume of a compound solid made of a cube and a pyramid, you need to calculate the volume of each shape separately and then add them together.

First, let's consider the cube. The volume of a cube is found using the formula \( V = a^3 \), where \( a \) is the length of one side of the cube. For example, if each side of the cube is 4 cm, the volume would be \( 4^3 = 64 \) cubic centimetres.

Next, let's look at the pyramid. The volume of a pyramid is given by the formula \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). If the base of the pyramid is a square with side length \( b \) and the height of the pyramid is \( h \), then the base area is \( b^2 \). For instance, if the side length of the base is 4 cm and the height is 6 cm, the volume would be \( \frac{1}{3} \times 4^2 \times 6 = \frac{1}{3} \times 16 \times 6 = 32 \) cubic centimetres.

Finally, to find the total volume of the compound solid, you simply add the volumes of the cube and the pyramid. Using our examples, the total volume would be \( 64 + 32 = 96 \) cubic centimetres. This method can be applied to any cube and pyramid combination by substituting the appropriate measurements into the formulas.