Answer:
Ratio of heights: 3 : 2
Ratio of surface areas: 9 : 4
Ratio of volumes: 27 : 8
Step-by-step explanation:
Since both cuboids are proportional, then we must derive expressions for the ratios of heights, surface areas and volumes from the following identities:
Perimeter
(1)
Surface area
(2)
Volume
(3)
Where:
, - Perimeters of the small cuboid and the big cuboid, in inches.
, - Surface areas of the small cuboid and the big cuboid, in square inches.
, - Volumes of the small cuboid and the big cuboid, in cubic inches.
By means of geometry formulas we expand the system of equations below:
Perimeter
Surface area
Volume
Where .
If we know that and , then we proceed to calculate all the ratios: