Step-by-step explanation:
The volume of the rectangular prism = l × b × h
= 1 1/2 × 1 × 2 1/2
= 3/2 × 5/2
= 15/4 feet³
The volume of the small cube = (1/2)³
= 1³/2³
= 1/8 foot³
To find:
How many small cubes fit in the rectangular prism?
15/4 ÷ 1/8
15/4 × 8
15 × 2
30
Therefore, 30 small cubes can fit inside the rectangular prism.
The volume of the rectangular prism in terms of the small cube
= 1/8 × 30
= 1/4 × 15
= 15/4 feet³
Number of small cubes that can be packed in the prism is 30 small cubes
The volume of the rectangular prism in terms of the small cube and a unit cube is 15/4 ft^3
The formula for calculating the volume of a rectangular prism is expressed as:
V = lwh
l is the length
w is the width
h is the height
Given the following
Length: 1 1/2 feet
Width: 1 foot
Height: 2 1/2 feet
V = 3/2 * 1 * 5/2
Volume = 15/4 ft^3
Similarly, for the cube;
Volume of the small cube = l³ = (1/2)³ = 1/8 ft^3
a) Number of small cubes that can be packed in the prism = 15/4 * 8
Number of small cubes that can be packed in the prism = 30 small cubes
b) The volume of the rectangular prism in terms of the small cube and a unit cube = 1/8 * 30 cubes
The volume of the rectangular prism in terms of the small cube and a unit cube is 15/4 ft^3
Learn more here: https://brainly.com/question/21214343
