Question

the diagram below represents a wooden model of a car in which the side window is an isosceles trapezoid. louis wants to carve a similar wooden model with smaller dimensions. the width of the smaller model will be 8 inches, with all other dimensions of the smaller model being proportional to the dimensions of the original model. the volume of the original model is 5280 cubic inches. what is the volume, v, of the new model to the nearest tenth of a cubic inch? 8 of 9 questions v≈307.2 cu in v≈337.9 cu in v≈460.8 cu in v≈483.8 cu in

Explanation:

Step1: Find the scale factor

The original width is \(20\) inches and the new width is \(8\) inches. The scale factor \(k=\frac{8}{20} = 0.4\)

Step2: Use the volume - scale factor relationship

For similar solids, if the scale factor of corresponding linear dimensions is \(k\), the scale factor of volumes is \(k^{3}\).
Let \(V_{1}\) be the volume of the original model and \(V_{2}\) be the volume of the new model. Then \(V_{2}=V_{1}\times k^{3}\)
We know that \(V_{1} = 5280\) and \(k = 0.4\)
So \(V_{2}=5280\times(0.4)^{3}\)
First, calculate \((0.4)^{3}=0.4\times0.4\times0.4=0.064\)
Then \(V_{2}=5280\times0.064 = 337.92\approx337.9\)

Answer:

\(V\approx337.9\) cu in