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Complete Question
A right rectangular prism with dimensions 1 5/8 inches by 1 1/2 inches by 1 3/8 inches is made up of small cubes with side lengths of 1/8 inch. How many 1/8 inch cubes make up the right rectangular prism?
a) 429
b) 858
c) 1287
d) 1716
Answer:
d) 1716 cubes
Step-by-step explanation:
Step 1
Find the volume of the rectangular the rectangular prism
Volume = Length × Width × Height
Length = 1 5/8 inches
Width = 1 1/2 inches
Height = 1 3/8 inches
Hence, Volume = 1 5/8 inches × 1 1/2 inches × 1 3/8 inches
= 13/8 inches × 3/2 inches × 11/8 inches
= 429/128 cubic inches
Step 2
We find the volume of 1 cube
Volume = (side length)³
= (1/8 Inches)³
= 1/8 × 1/8 × 1/8
=1/512 cubic inches
From the above question
The number of 1/8 inch cubes make up the right rectangular prism is calculated as:
= Volume of right rectangular prism ÷ Volume of 1 cube
(429/128)cubic inches ÷ (1/512) cubic inches
= 429/128 × 512/1
= 429 × 4
= 1716 cubes
Therefore, the number of cubes in the rectangular prism is 1716 cubes.
