3D Solids & Volume

The man would see 4 faces from the side view because a person's head typically has a front face, a left face, a right face, and a back face that are visible from the side.

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The volume of a cube is calculated by multiplying the length of one side by itself three times. In this case, the cube has a volume of 27 units cubed because 3 multiplied by itself three times equals 27.

The man would see 6 faces from his view from the top.

The volume of a rectangular prism is calculated by multiplying the length, width, and height together. In this case, the length is 4 cm, the width is 6 cm, and the height is 3 cm. By multiplying these values (4 x 6 x 3), we get the volume of 72 cm cubed.

The volume of a cube is calculated by multiplying the length, width, and height of the cube. Since all sides of a cube are equal, the height can be used as the length, width, and height of the cube. Therefore, the volume of a cube with a height of 5 inches is 5 x 5 x 5 = 125 inches cubed.

A rectangular prism has 6 faces because it has 6 sides. It has 12 edges because each side of the rectangle has 2 edges, and there are 6 sides in total. It has 8 vertices because each corner of the rectangular prism is a vertex, and there are 8 corners in total.

The volume of a rectangular prism is calculated by multiplying the length, width, and height of the prism. Since the question specifically asks for the volume of the base layer, it means that the height of the prism is not included in the calculation. Therefore, the correct answer is 12 cm cubed, as it represents the volume of the base layer of the rectangular prism.

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The box on the left is not completely full like the box on the right. To make it completely full, we need to add more unit cubes. The correct answer is 39, which means that we need 39 more unit cubes to fill the box on the left.