Questions: Weight 1848 lbs Size : 3 ft × 4 ft × 5 ft What is the density of this object?

Solution Steps

First, we need to calculate the volume of the object using its dimensions. The volume \( V \) of a rectangular prism is given by: \[ V = \text{length} \times \text{width} \times \text{height} \] Given the dimensions: \[ V = 3 \, \text{ft} \times 4 \, \text{ft} \times 5 \, \text{ft} \] \[ V = 60 \, \text{ft}^3 \]

Since density is often expressed in pounds per cubic inch, we need to convert the volume from cubic feet to cubic inches. There are \( 12 \) inches in a foot, so: \[ 1 \, \text{ft}^3 = (12 \, \text{in})^3 = 1728 \, \text{in}^3 \] Thus, \[ V = 60 \, \text{ft}^3 \times 1728 \, \text{in}^3/\text{ft}^3 = 103680 \, \text{in}^3 \]

Density \( \rho \) is defined as mass divided by volume. Given the weight (mass) of the object is \( 1848 \) lbs and the volume is \( 103680 \, \text{in}^3 \): \[ \rho = \frac{\text{mass}}{\text{volume}} = \frac{1848 \, \text{lbs}}{103680 \, \text{in}^3} \] \[ \rho \approx 0.0178 \, \text{lbs/in}^3 \]

Final Answer