Tuesday 5.20 4. Sphere A has radius 2 cm . Sphere B has radiu 4 cm . a. Calculate the volume of each sphere.

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To calculate the volume of a sphere, you can use the following formula:

$$
V = \frac{4}{3} \pi r^3
$$

where:
- $$ V $$ is the volume of the sphere,
- $$ r $$ is the radius of the sphere,
- $$ \pi $$ is a mathematical constant approximately equal to 3.14159.

### a. Calculate the Volume of Each Sphere

**Sphere A:**
- **Radius ($$ r_A $$) = 2 cm**

$$
V_A = \frac{4}{3} \pi r_A^3 = \frac{4}{3} \pi (2\,\text{cm})^3 = \frac{4}{3} \pi (8\,\text{cm}^3) = \frac{32}{3} \pi \,\text{cm}^3 \approx 33.51\,\text{cm}^3
$$

**Sphere B:**
- **Radius ($$ r_B $$) = 4 cm**

$$
V_B = \frac{4}{3} \pi r_B^3 = \frac{4}{3} \pi (4\,\text{cm})^3 = \frac{4}{3} \pi (64\,\text{cm}^3) = \frac{256}{3} \pi \,\text{cm}^3 \approx 268.08\,\text{cm}^3
$$

### Summary of Volumes
- **Volume of Sphere A:** $$ \frac{32}{3} \pi \,\text{cm}^3 \approx 33.51\,\text{cm}^3 $$
- **Volume of Sphere B:** $$ \frac{256}{3} \pi \,\text{cm}^3 \approx 268.08\,\text{cm}^3 $$

These calculations provide both the exact volume in terms of $$ \pi $$ and the approximate numerical values.
The volume of Sphere A is $$ \frac{32}{3} \pi $$ cm³ (approximately 33.51 cm³), and the volume of Sphere B is $$ \frac{256}{3} \pi $$ cm³ (approximately 268.08 cm³).

Tuesday 5.20 4. Sphere A has radius 2 cm . Sphere B has radiu 4 cm . a. Calculate the volume of each sphere.

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