Calculate the composite solid consisting of a cube of edge,28cm and a square based pyramid of height 16cm.calculate the volume of the solid.
Assuming the pyramid sits on top of the cube ....
Vol = 28^3 + (1/3)(28^2)(16) cm^3
= ...
To calculate the volume of the composite solid consisting of a cube and a square-based pyramid, we need to determine the volume of each individual shape and then add them together.
First, let's calculate the volume of the cube:
The cube has an edge length of 28 cm. The formula for the volume of a cube is V = s^3, where s is the length of an edge.
Substituting the value of 28 cm for s, we get V_cube = 28^3 = 21,952 cm^3.
Next, let's calculate the volume of the square-based pyramid:
The square-based pyramid has a height of 16 cm. To calculate the volume, we need to find the area of the base and then multiply it by one-third of the height. The formula for the volume of a pyramid is V = (1/3) * base area * height.
The base of the pyramid is a square, and the formula for finding the area of a square is A = s^2, where s is the length of a side.
Since the pyramid and cube share the same base, the length of the side of the square base is the same as the edge length of the cube, which is 28 cm.
Substituting the values into the formula, we get V_pyramid = (1/3) * 28^2 * 16 = 12,288 cm^3.
Now, to calculate the volume of the composite solid, we simply add the volumes of the cube and the square-based pyramid:
V_composite = V_cube + V_pyramid
V_composite = 21,952 cm^3 + 12,288 cm^3
V_composite = 34,240 cm^3
Therefore, the volume of the composite solid consisting of a cube with an edge length of 28 cm and a square-based pyramid with a height of 16 cm is 34,240 cm^3.