Question

A rectangular prism is made up of 36 unit cubes. The prism is 3 unit cubes high.

Choose two sets that could be the width and the length of the rectangular prism.
A. width: 2 unit cubes
length: 6 unit cubes
B. width: 3 unit cubes
length: 12 unit cubes
C. width: 4 unit cubes
length: 3 unit cubes
D. width: 5 unit cubes
length: 7 unit cubes
E. width: 6 unit cubes
length: 6 unit cubes

Answer 1

A. width: 2 unit cubes, length: 6 unit cubes and C. width: 4 unit cubes, length: 3 unit cubes.

Explanation:

To find the possible sets of width and length of the rectangular prism, we need to consider that the total number of unit cubes is 36 and the prism is 3 unit cubes high. Therefore, the volume of the prism is 36 cubic units. We can check each of the options to see if they satisfy the criteria:

A. width: 2 unit cubes, length: 6 unit cubes

Volume = width x length x height = 2 x 6 x 3 = 36 cubic units (matches the given criteria)

B. width: 3 unit cubes, length: 12 unit cubes

Volume = width x length x height = 3 x 12 x 3 = 108 cubic units (does not match the given criteria)

C. width: 4 unit cubes, length: 3 unit cubes

Volume = width x length x height = 4 x 3 x 3 = 36 cubic units (matches the given criteria)

D. width: 5 unit cubes, length: 7 unit cubes

Volume = width x length x height = 5 x 7 x 3 = 105 cubic units (does not match the given criteria)

E. width: 6 unit cubes, length: 6 unit cubes

Volume = width x length x height = 6 x 6 x 3 = 108 cubic units (does not match the given criteria)

Therefore, the possible sets of width and length of the rectangular prism are A. width: 2 unit cubes, length: 6 unit cubes and C. width: 4 unit cubes, length: 3 unit cubes.