Question

If the density of the wood is 3 pounds per cubic foot and if the weight of the solid is 360 pounds, what is the width, $\mathrm{w},$ in feet, of the solid? $$\begin{array}{l}{\text { (A) } 5.0} \\ {\text { (B) } 2.5} \\ {\text { (C) } 2.4} \\ {\text { (D) } 1.5}\end{array}$$

Name: Problem 23, Chapter :
Uploaded: 2019-05-02T16:29:14-08:00
Duration: 1 min 47 s
Channel: Lily An
Description: If the density of the wood is 3 pounds per cubic foot and if the weight of the solid is 360 pounds, what is the width, w, in feet, of the solid? (A) 5.0 (B) 2.5 (C) 2.4 (D) 1.5

   If the density of the wood is 3 pounds per cubic foot and if the
weight of the solid is 360 pounds, what is the width, $\mathrm{w},$ in feet, of
the solid?
$$\begin{array}{l}{\text { (A) } 5.0} \\ {\text { (B) } 2.5} \\ {\text { (C) } 2.4} \\ {\text { (D) } 1.5}\end{array}$$

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Solved by Expert Lily An

05/02/2019

Step 1

Step 1: We know that the density of a substance is given by the formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] where mass is in pounds and volume is in cubic feet. Show more…

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If the density of the wood is 3 pounds per cubic foot and if the weight of the solid is 360 pounds, what is the width, $\mathrm{w},$ in feet, of the solid? $$\begin{array}{l}{\text { (A) } 5.0} \\ {\text { (B) } 2.5} \\ {\text { (C) } 2.4} \\ {\text { (D) } 1.5}\end{array}$$

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Key Concepts

Density

Density is a measure of how much mass (or weight) is contained in a given volume. It is calculated by dividing the weight of an object by its volume, and provides a fundamental relationship used to link physical properties of materials.

Volume

Volume is the measure of space occupied by a three-dimensional object. In many problems involving solids, determining the volume is essential because it relates directly to other properties like weight when combined with the density.

Algebraic Manipulation

Algebraic manipulation involves setting up and solving equations that relate different physical quantities. In such problems, using the formula weight = density × volume, one can isolate an unknown dimension by performing the necessary algebraic steps, ensuring the correct units and relationships are maintained.

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