I am having trouble with this question. I have no idea what to do.
A miniature box used a scale model of a building of a shape of a right rectangular prism. The prism has edge lengths of 2 1/2 inches, 2 1/8 inches, and 1 inch. How many cubes with side lengths of 1/8 inch would be needed to fill the prism?
What is the volume of the prism? Show your work.
the prism is 20 cubes by 17 cubes by 8 cubes
cubes = 20 * 17 * 8
vol = 2 1/2 * 2 1/8 * 1 in^3
( 2 1 / 2 ) / ( 1 / 8 ) = 2.5 / 0.125 = 20
( 2 1 / 8 ) / ( 1 / 8 ) = 2.125 / 0.125 = 17
1 / ( 1 / 8 ) = 1 / 0.125 = 8
20 * 17 * 8 = 2720 cubes
OR
Volume of a right rectangular prism:
V = 2 1/2 * 2 1/8 * 1 = 2.5 * 2.125 * 1 = 5.3125 in ^ 3
Volume of a cube:
V = ( 1 / 8 ) ^ 3 = 0.125 ^ 3 = 0.001953125 in ^ 3
5.3125 / 0.001953125 = 2720 cubes
To find the volume of the right rectangular prism, you need to multiply the length, width, and height of the prism.
Given dimensions:
Length: 2 1/2 inches
Width: 2 1/8 inches
Height: 1 inch
To multiply mixed numbers like these, convert them into improper fractions:
2 1/2 = (2 * 2) + 1/2 = 5/2
2 1/8 = (2 * 8) + 1/8 = 17/8
Now, multiply the fractions:
Volume = (5/2) * (17/8) * 1
First, multiply the numerators (5 * 17 = 85) and the denominators (2 * 8 = 16):
Volume = (85/16) * 1
Since you're multiplying a fraction by a whole number, you can write the whole number as a fraction with a denominator of 1:
Volume = (85/16) * (1/1)
To multiply fractions, you simply multiply the numerators together and the denominators together:
Volume = 85/16
Therefore, the volume of the right rectangular prism is 85/16 cubic inches.
To calculate the number of cubes with side lengths of 1/8 inch needed to fill the prism, we need to divide the volume of the prism by the volume of a single cube.
The volume of a cube with side length 1/8 inch is (1/8) * (1/8) * (1/8) = 1/512 cubic inches.
Now, divide the volume of the prism (85/16) by the volume of a single cube (1/512):
Number of cubes needed = (85/16) / (1/512)
When dividing fractions, multiply the first fraction by the reciprocal of the second fraction:
Number of cubes needed = (85/16) * (512/1)
Multiply the numerators (85 * 512 = 43520) and the denominators (16 * 1 = 16):
Number of cubes needed = 43520/16
The number of cubes needed to fill the prism is 2719 cubes.