The sides of a cube is `8cm`. The volume of the cube with due respect to significant figure is

Options

A. `50cm^(3)`
B. `512cm^(3)`
C. `510cm^(3)`
D. `5.12xx10^(2)cm^(3)`

Answer

To find the volume of a cube with a side length of 8 cm and determine the significant figures, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the side length of the cube**:
The side length \( A \) of the cube is given as \( 8 \, \text{cm} \).

2. **Use the formula for the volume of a cube**:
The volume \( V \) of a cube is calculated using the formula:
\[ V = A^3 \]
where \( A \) is the length of a side of the cube.

3. **Calculate the volume**:
Substitute the value of \( A \) into the formula:
\[ V = 8^3 = 8 \times 8 \times 8 \]
Performing the multiplication:
\[ 8 \times 8 = 64 \]
\[ 64 \times 8 = 512 \]
Thus, the volume \( V \) is:
\[ V = 512 \, \text{cm}^3 \]

4. **Determine the significant figures**:
The original measurement of the side length \( 8 \, \text{cm} \) has 1 significant figure (the digit '8'). When calculating the volume, the result \( 512 \, \text{cm}^3 \) must be expressed with respect to the significant figures of the measurement used. Since the side length has 1 significant figure, the volume should also be reported with 3 significant figures.

5. **Express the volume in scientific notation**:
The volume can also be expressed in scientific notation:
\[ V = 5.12 \times 10^2 \, \text{cm}^3 \]
This representation also maintains the 3 significant figures.

### Final Answer:
The volume of the cube is \( 512 \, \text{cm}^3 \) or \( 5.12 \times 10^2 \, \text{cm}^3 \), both with 3 significant figures.