Subjects geometry

Volume Sphere

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Volume Sphere


1. The problem asks us to find the volume of a beach ball which is a sphere. 2. We are given the diameter of the sphere as 30 cm. To find the radius $r$, we use the relation: $$r = \frac{\text{diameter}}{2} = \frac{30}{2} = 15 \text{ cm}$$ 3. The formula for the volume $V$ of a sphere is: $$V = \frac{4}{3} \pi r^3$$ 4. Substitute $r = 15$ cm into the formula: $$V = \frac{4}{3} \pi (15)^3$$ 5. Calculate the cube of 15: $$15^3 = 15 \times 15 \times 15 = 3375$$ 6. Substitute back: $$V = \frac{4}{3} \pi \times 3375 = \frac{4}{3} \times 3375 \pi$$ 7. Multiply $\frac{4}{3} \times 3375$: $$\frac{4}{3} \times 3375 = 4 \times 1125 = 4500$$ 8. So the volume is: $$V = 4500 \pi \text{ cm}^3$$ The volume of the beach ball is $4500 \pi$ cubic centimeters, expressed in terms of $\pi$.