Maths,show a composite solid consisting of a cube of edge,28cm and a square based pyramid of height 16cm.calculate the volume of the solid.
the faces of the cube are 28^2
So is the base of the pyramid.
So, the composite volume is
28^3 + 1/3 * 28^2 * 16
Your school SUBJECT is MATH.
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To calculate the volume of the composite solid, we need to find the volumes of each individual 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 = s^3, where s is the length of the side.
Given that the edge of the cube is 28 cm, the volume of the cube is V_cube = 28^3.
V_cube = 28 × 28 × 28 = 21952 cm³
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.
Given that the height of the pyramid is 16 cm, we need to calculate the base area of the pyramid. Since the base of the pyramid is a square with the same edge length as the cube, the base area is equal to the side length squared.
Base area = (28 cm)^2 = 784 cm²
Now, let's calculate the volume of the pyramid:
V_pyramid = (1/3) × 784 cm² × 16 cm
V_pyramid = 1/3 × 784 × 16 cm³ = 13248 cm³
Finally, to find the volume of the composite solid, we add the volumes of the cube and the pyramid:
Total volume = V_cube + V_pyramid
Total volume = 21952 cm³ + 13248 cm³ = 35200 cm³
Therefore, the volume of the composite solid is 35200 cm³.