(c) A spherical ball of lead has a diameter of 5.0 cm. What is the mass of the sphere if lead has a density of 11.34 g>cm3? (The volume of a sphere is 14>32pr3, where r is the radius.)

Verified step by step guidance

1. Convert the diameter of the sphere to the radius by dividing the diameter by 2. The radius r = \frac{5.0 \text{ cm}}{2}.
2. Use the formula for the volume of a sphere: V = \frac{4}{3} \pi r^3. Substitute the radius into this formula to find the volume.
3. Calculate the volume of the sphere using the value of \pi \approx 3.14159.
4. Use the density formula: \text{Density} = \frac{\text{Mass}}{\text{Volume}}. Rearrange this to find the mass: \text{Mass} = \text{Density} \times \text{Volume}.
5. Substitute the density of lead (11.34 \text{ g/cm}^3) and the calculated volume into the mass formula to find the mass of the lead sphere.

Key Concepts

Density

Density is defined as mass per unit volume and is a key property of materials. It is typically expressed in grams per cubic centimeter (g/cm³) for solids and liquids. In this problem, the density of lead is given as 11.34 g/cm³, which will be used to calculate the mass of the lead sphere once its volume is determined.

Volume of a Sphere

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. The radius is half of the diameter, so for a sphere with a diameter of 5.0 cm, the radius would be 2.5 cm. This volume will be essential for finding the mass of the lead sphere using its density.

Mass Calculation

Mass can be calculated using the formula mass = density × volume. Once the volume of the sphere is calculated using the radius, and knowing the density of lead, this formula allows us to find the mass of the lead sphere. This relationship is fundamental in chemistry for converting between different properties of substances.