5 A prism is built with 48 cubes, each with an edge length of 1 cm . The base consists of 8 layers. What is the height
of the prism?

Question

5 A prism is built with 48 cubes, each with an edge length of 1 cm . The base consists of 8 layers. What is the height of the prism?

UpStudy AI · Accepted Answer

To find the height of the prism, we can follow these steps:

1. **Calculate the total volume of the prism**: Since each cube has an edge length of 1 cm, the volume of one cube is $$1^3 = 1 \, \text{cm}^3$$. Therefore, the total volume of the prism, which is made up of 48 cubes, is:
   $$
   V = 48 \, \text{cm}^3
   $$

2. **Determine the volume of the base**: The base consists of 8 layers of cubes. Since the total volume is 48 cm³ and there are 8 layers, the volume of the base can be calculated as:
   $$
   V_{\text{base}} = \frac{V}{\text{height}} = \frac{48}{h}
   $$
   where $$h$$ is the height of the prism.

3. **Calculate the height**: The height of the prism can be determined by dividing the total number of cubes by the number of layers:
   $$
   h = \frac{\text{Total number of cubes}}{\text{Number of layers}} = \frac{48}{8}
   $$

Now, let's calculate the height.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{48}{8}$$
- step1: Reduce the numbers:
  $$\frac{6}{1}$$
- step2: Calculate:
  $$6$$
The height of the prism is $$ 6 \, \text{cm} $$.

5 A prism is built with 48 cubes, each with an edge length of 1 cm . The base consists of 8 layers. What is the height
of the prism?

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