Questions: A solid metal sphere has a volume of 4.1 ft^3. The mass of the sphere is 795 lb. Find the density of the metal sphere in grams per cubic centimeter.

Solution Steps

First, we need to convert the volume from cubic feet to cubic centimeters. The conversion factor is: \[ 1 \, \text{ft}^3 = 28316.8466 \, \text{cm}^3 \]

Given volume: \[ 4.1 \, \text{ft}^3 \]

Convert to cubic centimeters: \[ 4.1 \, \text{ft}^3 \times 28316.8466 \, \text{cm}^3/\text{ft}^3 = 116099.0711 \, \text{cm}^3 \]

Next, we need to convert the mass from pounds to grams. The conversion factor is: \[ 1 \, \text{lb} = 453.5924 \, \text{g} \]

Given mass: \[ 795 \, \text{lb} \]

Convert to grams: \[ 795 \, \text{lb} \times 453.5924 \, \text{g}/\text{lb} = 360106.1580 \, \text{g} \]

Density is defined as mass per unit volume. Using the converted values: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

Substitute the values: \[ \text{Density} = \frac{360106.1580 \, \text{g}}{116099.0711 \, \text{cm}^3} = 3.1014 \, \text{g/cm}^3 \]

Final Answer