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.