Subjects geometry

Beach Ball Volume 8F903C

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1. **State the problem:** Find the volume of a beach ball with a diameter of 2 ft, using $\pi = 3.14$. 2. **Formula:** The volume $V$ of a sphere is given by $$V = \frac{4}{3} \pi r^3$$ where $r$ is the radius of the sphere. 3. **Calculate the radius:** Since the diameter is 2 ft, $$r = \frac{2}{2} = 1 \text{ ft}$$ 4. **Substitute values into the formula:** $$V = \frac{4}{3} \times 3.14 \times 1^3 = \frac{4}{3} \times 3.14 \times 1$$ 5. **Simplify:** $$V = \frac{4}{3} \times 3.14 = \frac{4 \times 3.14}{3}$$ 6. **Show cancellation:** $$V = \frac{\cancel{4} \times 3.14}{\cancel{3}} \times \frac{4}{3} \Rightarrow V = \frac{4 \times 3.14}{3}$$ (Note: No common factors to cancel between 4 and 3, so this step confirms the fraction.) 7. **Calculate the volume:** $$V = \frac{4 \times 3.14}{3} = \frac{12.56}{3} = 4.186666...$$ 8. **Round to the nearest tenth:** $$V \approx 4.2 \text{ ft}^3$$ **Final answer:** The volume of the beach ball is approximately **4.2 ft³**. This corresponds to option B.