A cone has a height of 17 inches and a diameter of 12 inches. What is its volume? Use \( \pi \approx 3.14 \) and round your answer to the nearest hundredth.
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To find the volume of the cone, you can use the formula: \[ V = \frac{1}{3} \pi r^2 h \] First, calculate the radius by taking half of the diameter, which is \( r = \frac{12}{2} = 6 \) inches. Then, substitute the values into the formula: \[ V = \frac{1}{3} \times 3.14 \times (6^2) \times 17 \] Calculating \( 6^2 \) gives \( 36 \). Now, substituting that back in: \[ V = \frac{1}{3} \times 3.14 \times 36 \times 17 \] Calculating further: \[ V \approx \frac{1}{3} \times 3.14 \times 612 = \frac{1}{3} \times 1926.48 \approx 642.16 \] So the volume of the cone is approximately **642.16 cubic inches**.
