A right rectangular prism has these dimensions:
Length: Fraction 1 and 1 over 4 units
Width: Fraction 5 over 8 unit
Height: Fraction 3 over 4 unit
How many unit cubes of side length Fraction 1 over 8 unit are required to pack the prism without any gap or overlap?
divide the total volume by the volume of one cube
(1 1/4)*(5/8)*(3/4) ÷ (1/8)^3 = 300
good practice for fractions here!
Or, express the dimensions in terms of how many cubes fit in each direction
1 1/4 = 5/4 = 10/8
3/4 = 6/8
So the prism's dimensions (in terms of cubes) are
10x5x6 = 300 cubes
1 1/4 and 1 8/6 and 1/4 i need help wth i cant get it
Amogus
can't yall figure this out I mean its 300
should be 300
All ik is thats its not 300 yall dumb
To find the number of unit cubes required to pack the prism without any gap or overlap, we need to calculate the volume of the prism and then divide it by the volume of each unit cube.
Step 1: Calculate the volume of the prism
The volume of a rectangular prism is given by the formula: Volume = Length x Width x Height.
Given:
Length = Fraction 1 and 1 over 4 units = 1 + 1/4 = 5/4 units
Width = Fraction 5 over 8 unit = 5/8 units
Height = Fraction 3 over 4 unit = 3/4 units
So, the volume of the prism = (5/4) x (5/8) x (3/4) = (25/32) cubic units.
Step 2: Calculate the volume of each unit cube
The volume of a cube is given by the formula: Volume = side length^3.
Given:
Side length of each unit cube = Fraction 1 over 8 unit = 1/8 units.
So, the volume of each unit cube = (1/8)^3 = 1/512 cubic units.
Step 3: Calculate the number of unit cubes required
To find the number of unit cubes required to pack the prism, we need to divide the volume of the prism by the volume of each unit cube.
Number of unit cubes required = (Volume of the prism) / (Volume of each unit cube)
= (25/32) / (1/512)
= (25/32) x (512/1)
= 25 x 512 / 32
= 800 unit cubes.
Therefore, you would require 800 unit cubes of side length Fraction 1 over 8 unit to pack the prism without any gap or overlap.