Ana finds the volume of a right rectangular prism with length 1/2, width 1 1/2 and height 2 cm using the cube method Find the volume of the prism using the formula method What awer should Ana get? Provide your answer as an improper fraction reduced to the lowest terms
cubic centimeters
Using the cube method, Ana would create a cube with side length equal to the greatest common factor of the dimensions, which in this case is 1/2 cm. Then she would count the number of smaller cubes that would fit inside the larger cube and multiply by the volume of each small cube, which is (1/2 cm)^3 = 1/8 cubic centimeters.
Since the length, width, and height are given in different units, we first need to convert them all to the same unit. 1/2 cm is equivalent to 0.5 cm and 1 1/2 cm is equivalent to 1.5 cm. The volume of the prism is then:
(0.5 cm) x (1.5 cm) x (2 cm) = 1.5 cubic centimeters
Therefore, Ana should get 1 1/2 or 3/2 cubic centimeters.
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To find the volume of a right rectangular prism using the cube method, you can imagine the prism as a stack of unit cubes.
First, let's find the total number of unit cubes that fit inside the prism. Since the length of the prism is 1/2 cm, the width is 1 1/2 cm, and the height is 2 cm, we need to consider the fractional lengths as well.
The length of the prism can be thought of as 1/2 unit cubes, the width can be thought of as 1.5 unit cubes, and the height can be thought of as 2 unit cubes.
To find the total number of unit cubes, we multiply the fractional lengths:
1/2 * 1 1/2 * 2 = 3/4 * 3/2 * 2 = 9/8
So, according to the cube method, Ana should get a volume of 9/8 cubic units.
Now, let's find the volume of the same prism using the formula method. The formula to find the volume of a rectangular prism is:
Volume = length * width * height
In this case, the length is 1/2 cm, the width is 1 1/2 cm, and the height is 2 cm.
When multiplying fractions and mixed numbers, it's best to convert the mixed number to an improper fraction:
1 1/2 = 3/2
Now, we can substitute the values into the formula:
Volume = 1/2 * 3/2 * 2
= 3/4 * 2
= 6/4
= 3/2
So, according to the formula method, Ana should also get a volume of 3/2 cubic units.
Therefore, Ana should get a volume of 9/8 cubic centimeters using the cube method and a volume of 3/2 cubic centimeters using the formula method.