A sphere with a mass of 12 g has a radius of 2 cm. What is its density?

• A. 0.72 g/cm^3
• B. 0.72 g/cm^3
• C. 0.36 g/cm^3
• D. 0.72 g/mL

Answer: (B)

Verified step by step guidance

1. Identify the formula for density, which is given by \(\text{density} = \frac{\text{mass}}{\text{volume}}\).
2. Note the given values: mass \(m = 12\) g and radius \(r = 2\) cm. Since the radius is in centimeters, the volume will be in cubic centimeters (cm\(^3\)), which is compatible with grams for density in g/cm\(^3\).
3. Calculate the volume of the sphere using the formula for the volume of a sphere: \(V = \frac{4}{3} \pi r^{3}\). Substitute \(r = 2\) cm into this formula.
4. Substitute the mass and the calculated volume into the density formula: \(\text{density} = \frac{12 \text{ g}}{V \text{ cm}^3}\).
5. Perform the division to find the density in g/cm\(^3\). This will give you the density of the sphere.