Final answer:
There are 150, 135, and 216 cubes of 1/10 foot in 5 yards (length), 4 1/2 yards (width), and 7 1/5 yards (height) respectively. To fill the larger prism completely, it would take 4,374,000 small prisms.
Step-by-step explanation:
For part a, there are 3 feet in a yard, so 5 yards equals 15 feet. Since each cube is 1/10 of a foot, we have 15 feet x 10 (1/10 cubes per foot) to get 150 1/10 cubes in length.
For part b, 4 1/2 yards is equal to 4.5 yards, which is 13.5 feet when converted (3 feet per yard). Thus, there are 13.5 feet x 10 (1/10 cubes per foot) giving us 135 1/10 cubes in width.
For part c, 7 1/5 yards is 7.2 yards or 21.6 feet, yielding 21.6 feet x 10 (1/10 cubes per foot) to give 216 1/10 cubes in height.
Lastly, for part d, to find out the total number of 1/10 cubes needed to fill the larger prism, multiply the number of cubes in length by width by height, so 150 x 135 x 216 to get 4,374,000 small prisms.