Question

unit 5 lesson 8 assignment
a scale model of an oil tanker truck can hold 1 gallon of oil
if a trucking company wants the full - size truck to hold 8,000 gallons of oil, what scale factor must they apply to the model?

Explanation:

Step1: Understand volume scale factor

The volume of a 3D object scales with the cube of the linear scale factor. Let the linear scale factor be \( k \). The volume of the model is \( V_m = 1 \) gallon, and the volume of the full - size truck is \( V_f=8000 \) gallons. The relationship between the volumes and the scale factor is \( V_f=k^{3}\times V_m \).

Step2: Solve for the scale factor

We know that \( V_m = 1 \) and \( V_f = 8000 \). Substituting into the formula \( V_f=k^{3}\times V_m \), we get \( 8000=k^{3}\times1 \), so \( k^{3}=8000 \). To find \( k \), we take the cube root of both sides. Since \( 20\times20\times20 = 8000 \), \( k=\sqrt[3]{8000}=20 \).

Answer:

The scale factor is 20.