A right rectangular prism 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?

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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

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.

step-by-step explanation:

42

step-by-step explanation: