a rectangular prism 3cm x 5cm x 6cm is painted and is then cut into 1cm^3 cubes. What is the total unpainted surface area of these cubes?

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Please help! I do not understand this question.

You can figure out how many sides of all the cubes are unpainted (a lot of work), or you can just strip off the outside layer of cubes. The outside of the remaining block has the same area as the insides of all the deleted cubes. Its area is thus

2*(1*3 + 1*4 + 3*4) = 38

Sure! Let's break down the question step by step.

First, we have a rectangular prism with dimensions 3cm x 5cm x 6cm. This means it has a length of 3cm, a width of 5cm, and a height of 6cm. Visualize a rectangular-shaped block.

Next, the rectangular prism is painted. This means that all of its surfaces are covered with paint, including the front, back, sides, top, and bottom.

Now, we need to cut this painted rectangular prism into 1cm^3 cubes. This means we are dividing the entire prism into smaller cubes, each with side length 1cm. Visualize small, equal-sized cubes that make up the larger rectangular prism.

Finally, we want to find the total unpainted surface area of these smaller cubes. This means we want to calculate the sum of all the surface areas of the individual cubes that were inside the rectangular prism.

To find the total unpainted surface area of the cubes, we need to consider how many cubes make up the rectangular prism and their individual surface areas.

Let's calculate it step by step:

1. Find the total number of cubes: Since the rectangular prism has dimensions 3cm x 5cm x 6cm, we need to multiply these dimensions to find the total number of cubes. So, multiply 3cm x 5cm x 6cm = 90 cubes.

2. Find the individual surface area of each cube: A cube has six faces, and each face is a square. Since each face has side length 1cm, the surface area of each face is 1cm x 1cm = 1 square centimeter. As there are six faces, the total surface area of each cube is 1cm^2 x 6 = 6 square centimeters.

3. Find the total unpainted surface area of the cubes: Multiply the total number of cubes (90) by the surface area of each cube (6 square centimeters): 90 cubes x 6 square centimeters = 540 square centimeters.

So, the total unpainted surface area of the 1cm^3 cubes is 540 square centimeters.

I hope this explanation helps you understand how to approach and solve this problem!