Question

An architect is designing a house. He wants the bedroom to have the dimensions of 10 ft by 6 ft by 7 ft. The architect doubles one dimension to create the den. Does that mean the den will have double the volume of the bedroom?

Answer 1

No, doubling one dimension of a rectangular solid will not double its volume.

Step-by-step explanation:

No, doubling one dimension of a rectangular solid will not double its volume.

To calculate the volume of a rectangular solid, we multiply the length, width, and height. In this case, the original bedroom has dimensions of 10 ft by 6 ft by 7 ft, resulting in a volume of 420 cubic feet. If the architect doubles one dimension to create the den, the new dimensions would be 20 ft by 6 ft by 7 ft. The new volume would be 840 cubic feet, which is double the original bedroom's volume.

Therefore, doubling one dimension of the rectangular solid doubles its volume.