Subjects geometry

Ice Cream Volume Cf51Df

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1. **State the problem:** We need to find the total volume of 8 hemisphere-shaped portions of ice cream, each with a diameter of 6 cm. 2. **Identify the formula:** The volume of a hemisphere is given by the formula: $$V = \frac{2}{3} \pi r^3$$ where $r$ is the radius of the hemisphere. 3. **Calculate the radius:** Given diameter $d = 6$ cm, the radius is: $$r = \frac{d}{2} = \frac{6}{2} = 3 \text{ cm}$$ 4. **Calculate the volume of one hemisphere:** Substitute $r = 3$ cm into the volume formula: $$V = \frac{2}{3} \pi (3)^3 = \frac{2}{3} \pi \times 27 = 18 \pi \text{ cm}^3$$ 5. **Calculate the total volume for 8 hemispheres:** Multiply the volume of one hemisphere by 8: $$V_{total} = 8 \times 18 \pi = 144 \pi \text{ cm}^3$$ 6. **Approximate the total volume:** Using $\pi \approx 3.1416$: $$V_{total} \approx 144 \times 3.1416 = 451.39 \text{ cm}^3$$ **Final answer:** The total volume of ice cream on the cone is approximately $451.39$ cubic centimeters.