A (rectangular) cuboid is a closed box which comprises of 3 pairs of rectangular faces that are parallel to each other and joined at right angles. It is also known as a right rectangular prism. It has 8 vertices, 6 faces, and 12 edges. A cube is a cuboid whose faces are all squares.
An cuboid has a volume of and a surface area of .
What is the volume of a cuboid?
The volume is .
The volume of an cuboid is how many times the volume of a cuboid?
The volume of an cuboid divided by the volume of a cuboid is
Thus, the answer is 12 times.
The area of each of the 6 faces of a cuboid has grown by a factor of 4 times. Then the volume of the cuboid has grown by a factor of how many times?
Let be the dimensions of the original cuboid. Then it has a volume of and a surface area of Now, let be the dimensions of the enlarged cuboid. Then we have
Multiplying the three equations gives
which implies that the new volume is 8 times the original.
Suppose that an cuboid has a surface area of 22, where and If and are all integers, what is the volume of the cuboid?
We know that an cuboid has a volume of and a surface area of For this problem, it is given that or
Without loss of generality, let and then gives
Since no other 3 distinct integers than 1, 2, and 3 can satisfy the volume of the cuboid is