Question

Use tables to give the answers to 3 significant figures.use the value 0.4971 for log where necessary calculate the volume of a cube of edge 8.24cm

Answer 1

To find the volume of a cube, you can use the formula:

\[
\text{Volume} = \text{edge}^3
\]

Given the edge length of the cube is \( 8.24 \, \text{cm} \), here is the calculation step by step:

### Step 1: Calculate the Volume

\[
\text{Volume} = (8.24 \, \text{cm})^3
\]

Calculating \( 8.24^3 \):

\[
8.24 \times 8.24 \times 8.24 = 8.24 \times 8.24 = 67.8176 \, \text{cm}^2 \quad (\text{first multiplication}) \\
67.8176 \times 8.24 = 558.3794 \, \text{cm}^3 \quad (\text{second multiplication})
\]

### Step 2: Round to Significant Figures

Now, round \( 558.3794 \, \text{cm}^3 \) to 3 significant figures:

\[
\text{Volume} \approx 558 \, \text{cm}^3
\]

### Final Result

\[
\text{The volume of the cube is } 558 \, \text{cm}^3.
\]

### Summary Table

| Edge Length (cm) | Volume (cm³) | Volume (3 SF) |
|-------------------|--------------|----------------|
| 8.24 | 558.3794 | 558 |

Thus, the final answer for the volume of the cube with an edge of \( 8.24 \, \text{cm} \) is \( 558 \, \text{cm}^3 \) when rounded to three significant figures.