Sure, let me guide you step by step through the solution to the given problem.
### Understanding the Problem
We need to find the mass of a granite block given its dimensions and the density of granite.
### Step-by-Step Solution
a. What do you need to calculate before you can find the mass?
Before we can find the mass of the granite block, we need to calculate its volume.
How do we calculate the volume?
The volume of a rectangular block can be found using the formula for the volume of a rectangular prism:
[tex]\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \][/tex]
Given the dimensions:
- Length = 20 cm
- Width = 10 cm
- Height = 5 cm
Plugging these values into the formula, we get:
[tex]\[ \text{Volume} = 20 \, \text{cm} \times 10 \, \text{cm} \times 5 \, \text{cm} \][/tex]
[tex]\[ \text{Volume} = 1000 \, \text{cm}^3 \][/tex]
So, the volume of the granite block is [tex]\(1000 \, \text{cm}^3\)[/tex].
What is that value? Include units in your answer.
The value we needed to calculate before finding the mass is the volume of the granite block, which is [tex]\(1000 \, \text{cm}^3\)[/tex].
b. How do you find the mass of the granite block?
Now that we have the volume, we can find the mass using the formula:
[tex]\[ \text{Mass} = \text{Density} \times \text{Volume} \][/tex]
Given:
- Density of granite = 2.7 g/cm³
- Volume of the block = [tex]\(1000 \, \text{cm}^3\)[/tex]
Plugging these values into the formula, we get:
[tex]\[ \text{Mass} = 2.7 \, \text{g/cm}^3 \times 1000 \, \text{cm}^3 \][/tex]
[tex]\[ \text{Mass} = 2700 \, \text{g} \][/tex]
So, the mass of the piece of granite is [tex]\(2700 \, \text{g}\)[/tex].
