Question

The figure below shows a rectangular prism and a cube:

A rectangular prism and a cube are drawn side by side. The length of the rectangle prism is 6 inches, the width is 5 over 6 inch, and its height is 1 and 2 over 6 inches. The cube has a side length of 1 over 6 inch.

How many such cubes are required to completely pack the prism without any gap or overlap? (5 points)

a
240
b
900
c
1,440
d
3,658

Answer 1

Step-by-step explanation:

Given A rectangular prism and a cube are drawn side by side. The length of the rectangle prism is 6 inches, the width is 5 over 6 inch, and its height is 1 and 2 over 6 inches. The cube has a side length of 1 over 6 inch.

• How many such cubes are required to completely pack the prism without any gap or overlap?  
• Given L= 6 inches
•                W = 5/6 inches
•                 h = 1 2/6 inches = 8/6 = 4/3 inches
• So Volume of the prism V = LWh
•                                        V = 6 x 5/6 x 8/6
•                                       V = 20 / 3 cu inches
•                          Given cube has a length =  1/6 inches
• SO Volume of the cube V = b^3      
•                                              = (1/6)^3
•                                             = 1/216 cu inches
• We need to find the number of cubes.
•            So volume of the prism / volume of the cube
•                         = 20/3 / 1/216  
•                         = 1440 cubes.

Reference link will be

https://brainly.com/question/4187188