Small cubes with edge lengths of 1/4 inch will be packed into the right rectangular prism. The dimensions are 4 1/2 inches in length, 5 inches in width, and 3 3/4 inches in height. Each cube is 1/4 inches. How many small cubes are needed to completely fill the right rectangular prism? I have been trying to figure this problem out for over 3 hours. I know the answer is 5400,but I have no Idea of how to do the problem. I've tried every possibility that I could think of. Please help me. I'm so frustrated. Thank you

Let's see how many cubes we can lay along the length,

4.5 ÷ .25 = 18
and along the width,
5 ÷ .25 = 20
and how high can we stock them?
3.75 ÷ .25 = 15

So there would be 18 x 20 x 15 of them or 5400

(and you spent 3 hours on this? not possible!)

another way:
volume of 1 cube = .25^3 = .015625
volume box = (4.5)(5)(3.75) = 84.375

number of cubes = 84.375/.015625 = 5400

5+5=10

Thanks for the help!

I understand that you're feeling frustrated with this problem, but don't worry! I'll walk you through the steps to solve it.

To find the number of small cubes needed to completely fill the right rectangular prism, we need to calculate the volume of the prism and then divide it by the volume of one small cube.

Step 1: Calculate the volume of the prism
The volume of a rectangular prism is given by the formula: volume = length * width * height.

In this case, the length is 4 1/2 inches, which can be written as 4.5 inches.
The width is 5 inches.
The height is 3 3/4 inches, which can be written as 3.75 inches.

So, the volume of the prism is: 4.5 inches * 5 inches * 3.75 inches = 84.375 cubic inches.

Step 2: Calculate the volume of one small cube
The volume of a cube is given by the formula: volume = edge length * edge length * edge length.

In this case, the edge length of one small cube is 1/4 inch.

So, the volume of one small cube is: (1/4 inch) * (1/4 inch) * (1/4 inch) = 1/64 cubic inches.

Step 3: Divide the volume of the prism by the volume of one small cube
To find the number of small cubes needed to fill the prism, we divide the volume of the prism by the volume of one small cube.

84.375 cubic inches ÷ (1/64 cubic inches) = 84.375 * 64 = 5400 small cubes.

Therefore, you would need 5400 small cubes to completely fill the right rectangular prism.

I hope this explanation helps you understand the steps to solve this problem. Let me know if you have any further questions!