How many 1/2
inch cubes would fit inside a right rectangular prism with a length of 2 inches, a width of 1 1/2 i inches, and a height of 3inches
We first need to find the volume of the right rectangular prism. The formula for volume is:
Volume = length x width x height
Plugging in the values given, we get:
Volume = 2 inches x 1 1/2 inches x 3 inches
Volume = 9 cubic inches
Now, we need to find how many 1/2 inch cubes would fit in this space. We can do this by dividing the volume of the rectangular prism by the volume of each 1/2 inch cube. The formula for the volume of a cube is:
Volume = (length of side)³
Plugging in the value of 1/2 inch for the length of each side, we get:
Volume = (1/2 inch)³
Volume = 1/8 cubic inches
Now we can divide the volume of the rectangular prism by the volume of each 1/2 inch cube:
9 cubic inches ÷ (1/8 cubic inches per cube) = 72 cubes
Therefore, 72 1/2 inch cubes would fit inside the right rectangular prism.
or, the dimensions of the prism, in terms of 1/2" cubes, are
4 by 3 by 6 so the volume is 4*3*6 = 12 cubes
This is incorrect. If the dimensions of the prism were 4 by 3 by 6 cubes, then its volume would be:
Volume = 4 cubes x 3 cubes x 6 cubes = 72 cubic cubes
However, the volume of the prism is actually 9 cubic inches, as calculated earlier. Therefore, your dimensions of 4 by 3 by 6 cubes do not match the given dimensions of the prism, which are 2 inches by 1 1/2 inches by 3 inches.
It is important to carefully read and understand the given information before attempting to solve a problem.
yeah, my mistake - I made a typo when I said 12 cubes instead of 72 cubes.
I see. Thank you for clarifying. In any case, it's always important to carefully check our work and make sure the answers we give are accurate and match the given information.
To find out how many 1/2 inch cubes would fit inside the right rectangular prism, we need to determine the volume of the prism and then divide it by the volume of each 1/2 inch cube.
The volume of a right rectangular prism can be calculated by multiplying its length, width, and height. In this case, the length is 2 inches, the width is 1 1/2 inches, and the height is 3 inches.
First, we need to convert the width to a mixed number. 1 1/2 can be written as 3/2 inches.
Now, we can calculate the volume of the prism:
Volume = length × width × height
Volume = 2 inches × (3/2 inches) × 3 inches
Volume = 6 cubic inches
The volume of each 1/2 inch cube is 1/2 × 1/2 × 1/2 = 1/8 cubic inches.
To find out how many 1/2 inch cubes would fit inside the prism, we divide the volume of the prism by the volume of each cube:
6 cubic inches ÷ (1/8 cubic inches/cube)
6 cubic inches ÷ (1/8 cubic inches) × (8 cube/cubic inch)
6 ÷ 1 × 8 cubes
48 cubes
So, 48 1/2 inch cubes would fit inside the right rectangular prism.