Question

Pamela's parakeet is currently in a rectangular bird cage that has a length of 3 feet, a width of 2 feet, and a height of 3 feet. Since the parakeet has gotten larger, Pamela is looking to buy a new rectangular bird cage. She wants the new cage to have a volume that is 4 times the volume of the parakeet's current cage. If Pamela wants to keep the length of the new cage the same, how must the other dimensions change?

Answer 1

The volume of existing cage = length x widht x height = 3 x 2 x 3 = 18 cubic ft

Now she wants cage with volume four times of this cage

New Volume = V1 = 18 x 4 = 72 cubic ft

Keeping length same = 3 ft

Length x width x height = V1

3 x Width x height = 72

Width x height = 72 /3

Width x height = 24

Now multiple of 24 must be the width and height.

Taking width = 6 ft and height = 4 ft, we will get our answer

Proof:

Length x width x height = V1

3 x 6 x 4 = 72