Part A
A right rectangular prism has sides lengths of 4 inches, 3 1/2 inches, and 6 1/2 inches. How many 1/2 inch cubes would be needed to fill the prism?
Part B
What is the volume of the prism in Part A? Explain your answer.
8 * 7 * 13
volume is that over 8 because each cube is (1/2)(1/2)(1/2) or 1/8 in^3
Part A:
To find out how many 1/2 inch cubes are needed to fill a right rectangular prism, we need to determine the volume of the prism and then divide it by the volume of each individual 1/2 inch cube.
Part B:
The volume of a right rectangular prism can be found by multiplying its length, width, and height. In this case, the sides lengths given are:
Length = 4 inches
Width = 3 1/2 inches
Height = 6 1/2 inches
To convert the mixed fraction (3 1/2) to an improper fraction, we multiply the whole number (3) by the denominator (2) and add the numerator (1). This gives us 7/2.
Now, we can calculate the volume by multiplying the side lengths together:
4 inches * 7/2 inches * 6 1/2 inches
First, we simplify the mixed fraction of 6 1/2 to an improper fraction of 13/2:
4 inches * 7/2 inches * 13/2 inches
Next, we multiply the numerators together and the denominators together:
(4 * 7 * 13) / (2 * 2 * 2)
This simplifies to:
(4 * 7 * 13) / 8
Now, we calculate the product of the numerators:
4 * 7 * 13 = 364
Finally, we divide the product of the numerators by the product of the denominators:
364 / 8 = 45 1/2
So, the volume of the prism is 45 1/2 cubic inches.
Now, to find out how many 1/2 inch cubes are needed to fill the prism, we divide the volume of the prism by the volume of each individual 1/2 inch cube. The volume of a cube can be found by multiplying its side length by itself three times (length * width * height), which in this case is:
1/2 inch * 1/2 inch * 1/2 inch
Multiplying the fractions together:
(1/2 * 1/2 * 1/2) = 1/8
To find out how many 1/2 inch cubes fit into the prism, we divide the volume of the prism by the volume of each individual cube:
45 1/2 cubic inches / 1/8 cubic inches = 45 1/2 * 8 = 364
So, 364 1/2 inch cubes would be needed to fill the prism.