calculate the volume of the solid when the composite of a cube of edge is 28cm and the square -based pyramid of it height is 16cm
cube: 28^3
pyramid: (1/3)(28^2)(16)
now just add 'em up
To calculate the volume of the solid formed by the composite of a cube and a square-based pyramid, we need to find the volumes of each shape and then add them together.
First, let's calculate the volume of the cube. The formula for the volume of a cube is V = (edge)^3. In this case, the edge of the cube is 28 cm. So, the volume of the cube is V_cube = (28 cm)^3.
Next, let's calculate the volume of the square-based pyramid. The formula for the volume of a pyramid is V = (1/3) * (base area) * height. In this case, the height of the pyramid is 16 cm. To find the base area of the pyramid, we need to calculate the area of the square base. Since the edge of the cube is equal to the base length of the pyramid, the base area is (28 cm)^2. So, the volume of the pyramid is V_pyramid = (1/3) * (28 cm)^2 * 16 cm.
Finally, we can find the volume of the solid by adding the volumes of the cube and pyramid together. V_solid = V_cube + V_pyramid.
Let's calculate the volume of the solid:
V_cube = (28 cm)^3 = 28 cm * 28 cm * 28 cm = 21,952 cm^3
V_pyramid = (1/3) * (28 cm)^2 * 16 cm = 2,048 cm^3
V_solid = V_cube + V_pyramid = 21,952 cm^3 + 2,048 cm^3 = 24,000 cm^3
Therefore, the volume of the solid formed by the composite of a cube with an edge of 28 cm and a square-based pyramid with a height of 16 cm is 24,000 cm^3.