1. **State the problem:** We need to find the volume of a gold bar shaped like a rectangular prism with dimensions 6 in. × 2 \frac{7}{8} in. × 1 \frac{1}{2} in., then use the formula $w \approx 11.15n$ to find the weight in ounces, and finally calculate the value of the gold bar given the price per ounce is 1179. 2. **Calculate the volume:** Convert mixed numbers to improper fractions or decimals: $2 \frac{7}{8} = 2 + \frac{7}{8} = 2.875$ $1 \frac{1}{2} = 1 + \frac{1}{2} = 1.5$ Volume $n = 6 \times 2.875 \times 1.5$ 3. **Multiply step-by-step:** $6 \times 2.875 = 17.25$ Then, $17.25 \times 1.5 = 25.875$ So, volume $n \approx 25.875$ cubic inches. 4. **Find the weight using the formula:** $w \approx 11.15n = 11.15 \times 25.875$ Calculate: $11.15 \times 25.875 = 288.35625$ Rounded to nearest hundredth: $w \approx 288.36$ ounces. 5. **Calculate the value of the gold bar:** Value $= 288.36 \times 1179 = 339,885.24$ 6. **Final answer:** The volume of the gold bar is about 25.88 in$^3$, the weight is approximately 288.36 ounces, and the gold bar is worth about 339885.24.