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 $\pi$.