a solid cube has side length 3 inches. a 2-inch by 2-inch square hole is cut into the center of each face. the edges of each cut are parallel to the edges of the cube, and each hole goes all the way through the cube. what is the volume, in cubic inches, of the remaining solid?



Answer :

The volume of remaining solid is 7 in³.

What is volume of cube?

The whole three-dimensional area occupied by a cube is its volume.

A cube is a solid 3-D object with six square faces and equal-length sides.

The cube is one of the five platonic solid shapes and is also referred to as a regular hexahedron.

The cubic units are used to represent the cube's volume.

Imagine performing each cut individually.

A box 2*2*3 is eliminated in the initial cut. Two boxes with dimensions of 2*2*0.5 are removed during the second cut, and the third cut eliminates the same number of boxes on the final two faces.

Therefore, the sum of all cuts is 12 + 4 + 4 = 20.

∴Volume of rest of cube = 3³-20

                                         = 7 in³

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