Final answer:
To find the volume of the shape formed from a pyramid and a cuboid, calculate the volumes of each individually and then add them together. The volume of the pyramid is 6 cm³ and the volume of the cuboid is 24 cm³. Adding them together gives a total volume of 30 cm³.
Step-by-step explanation:
To find the volume of the shape formed from a pyramid and a cuboid, we need to calculate the volumes of each component separately and then add them together. Let's calculate the volume of the pyramid and the cuboid:
Pyramid:
The volume of a pyramid is given by the formula V = (1/3) * base area * height.
In this case, the base is a triangle, and its area is (1/2) * base * height.
The height of the pyramid is the slant height of the triangular face. Let's assume it is 3 cm.
The base of the triangle can be calculated using the Pythagorean Theorem, giving us a base length of 4 cm.
Plugging these values into the formula, we get V = (1/3) * (1/2) * 4 cm * 3 cm * 3 cm = 6 cm³.
Cuboid:
The volume of a cuboid is given by the formula V = length * width * height.
In this case, the length is 4 cm, the width is 2 cm, and the height is 3 cm.
Plugging in these values, we get V = 4 cm * 2 cm * 3 cm = 24 cm³.
Now, let's add the volumes of the pyramid and the cuboid together:
Total volume = 6 cm³ + 24 cm³ = 30 cm³.
Therefore, the volume of the shape formed from the pyramid and the cuboid is 30 cm³.