Question: What is the volume of the block?
Given:
$g = 9.8$ m/s²
$\rho_{water} = 1000$ kg/m³
$F_b = 18.12$ N
Unknown:
$V_{block} = ?$
Equation:
$F_b = \rho g V$
1. **State the problem:** We need to find the volume $V_{block}$ of a block given the buoyant force $F_b$, gravitational acceleration $g$, and the density of water $\rho_{water}$.
2. **Write the formula:** The buoyant force formula is $$F_b = \rho g V$$ where
- $F_b$ is the buoyant force,
- $\rho$ is the density of the fluid (water here),
- $g$ is the acceleration due to gravity,
- $V$ is the volume of the displaced fluid, which equals the volume of the block submerged.
3. **Rearrange the formula to solve for volume $V$:**
$$V = \frac{F_b}{\rho g}$$
4. **Substitute the known values:**
$$V = \frac{18.12}{1000 \times 9.8}$$
5. **Calculate the denominator:**
$$1000 \times 9.8 = 9800$$
6. **Calculate the volume:**
$$V = \frac{18.12}{9800}$$
7. **Simplify the fraction:**
$$V = \frac{\cancel{18.12}}{\cancel{9800}} = 0.00184898...$$
8. **Final answer:**
$$V \approx 0.00185 \text{ cubic meters}$$
This means the volume of the block is approximately $0.00185$ m³.