A sphere of radius 2cm has a mass of 11.2g, find its volume , it's density, and the mass of the sphere made of the same material with radius 3cm and properly explan along the way

The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$.

$$V_1 = \frac{4}{3} \times \pi \times (2 \text{ cm})^3$$ $$V_1 = \frac{4}{3} \times \pi \times 8 \text{ cm}^3$$ $$V_1 = \frac{32}{3}\pi \text{ cm}^3$$

Using $\pi \approx 3.14159$:

$$V_1 \approx \frac{32}{3} \times 3.14159 \text{ cm}^3$$ $$V_1 \approx 10.6667 \times 3.14159 \text{ cm}^3$$ $$V_1 \approx 33.51 \text{ cm}^3$$

The volume of the first sphere is $\boxed{33.51 \text{ cm}^3}$.

Density ($\rho$) is mass divided by volume ($\rho = \frac{m}{V}$).

$$\rho = \frac{m_1}{V_1}$$ $$\rho = \frac{11.2 \text{ g}}{33.51 \text{ cm}^3}$$ $$\rho \approx 0.3342 \text{ g/cm}^3$$

The density of the material is $\boxed{0.3342 \text{ g/cm}^3}$.

The second sphere has a radius of 3 cm.

$$V_2 = \frac{4}{3} \times \pi \times (3 \text{ cm})^3$$ $$V_2 = \frac{4}{3} \times \pi \times 27 \text{ cm}^3$$ $$V_2 = 4 \times \pi \times 9 \text{ cm}^3$$ $$V_2 = 36\pi \text{ cm}^3$$

Using $\pi \approx 3.14159$:

$$V_2 \approx 36 \times 3.14159 \text{ cm}^3$$ $$V_2 \approx 113.10 \text{ cm}^3$$

The volume of the second sphere is $\boxed{113.10 \text{ cm}^3}$.

Since the second sphere is made of the same material, it has the same density ($\rho$).
Mass ($m_2$) = Density ($\rho$) $\times$ Volume ($V_2$).

$$m_2 = 0.3342 \text{ g/cm}^3 \times 113.10 \text{ cm}^3$$ $$m_2 \approx 37.80 \text{ g}$$

The mass of the second sphere is $\boxed{37.80 \text{ g}}$.