Question

practice 4 (from unit 5, lesson 7)
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?
type your answer in the box.

Explanation:

Step1: Understand volume scale factor

The volume of a 3D object scales with the cube of the linear scale factor. Let the 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. Since \( V_f = k^{3}\times V_m \)

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 \( 8000=k^{3}\times1 \). To find \( k \), we take the cube root of both sides. \( k=\sqrt[3]{8000} \). Since \( 20\times20\times20 = 8000 \), \( \sqrt[3]{8000}=20 \)

Answer:

20