A barrel of oil has a height of 3 m and a diameter of 0.9 m . a) Estimate the volume of the oil in the barrel in metric units by rounding the diameter to the nearest meter and using 3 for $$ \pi $$. (Use $$ \mathrm{V}=\pi \mathrm{r}^{2} \mathrm{~h} $$.) b) Compute the actual volume of oil in the barrel. (Use $$ \mathrm{V}=\pi \mathrm{r}^{2} \mathrm{~h} $$.) a) The estimated volume of oil in the barrel is $$ 2.25 \mathrm{~m}^{3} $$. (Type an integer or a decimal.) b) The actual volume of oil in the barrel is about

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To compute the actual volume of oil in the barrel, we'll use the formula for the volume of a cylinder:

$$
\mathrm{V} = \pi r^{2} h
$$

**Given:**
- **Height (h):** 3 meters
- **Diameter (d):** 0.9 meters
- **Radius (r):** $$ \frac{d}{2} = \frac{0.9}{2} = 0.45 $$ meters
- **$$\pi$$:** Approximately 3.141592653589793

**Calculation:**

1. **Calculate $$ r^{2} $$:**
   $$
   r^{2} = (0.45)^2 = 0.2025 \, \text{m}^2
   $$

2. **Multiply by height (h):**
   $$
   r^{2} \times h = 0.2025 \times 3 = 0.6075 \, \text{m}^3
   $$

3. **Multiply by $$\pi$$ to get the volume:**
   $$
   \mathrm{V} = \pi \times 0.6075 \approx 3.141592653589793 \times 0.6075 \approx 1.9085 \, \text{m}^3
   $$

**Rounded to two decimal places:**
$$
\mathrm{V} \approx 1.91 \, \text{m}^3
$$

---

**Final Answer:**

b) The actual volume of oil in the barrel is about **1.91 m³**.
The actual volume of oil in the barrel is about 1.91 m³.

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