Question

a rectangular prism has a length of 4.2 cm, a width of 5.8 cm, and a height of 9.6 cm. a similar prism has a length of 14.7 cm, a width of 20.3 cm, and a height of 33.6 cm. the dimensions of the smaller prism are each multiplied by what factor to produce the corresponding dimensions of the larger prism? \\(\bigcirc\\) \\(3\frac{1}{2}\\) \\(\bigcirc\\) 4 \\(\bigcirc\\) \\(4\frac{5}{6}\\) \\(\bigcirc\\) 5

Explanation:

Step1: Calculate the ratio for length

For similar prisms, the scale factor \(k\) can be found by dividing the corresponding dimension of the larger prism by the smaller prism. For length: \(k=\frac{14.7}{4.2}\)

$$ \frac{14.7}{4.2}=\frac{147}{42}=\frac{7}{2}=3\frac{1}{2} $$

Step2: Verify with width

Check with width: \(\frac{20.3}{5.8}=\frac{203}{58}=\frac{7}{2}=3\frac{1}{2}\)

Step3: Verify with height

Check with height: \(\frac{33.6}{9.6}=\frac{336}{96}=\frac{7}{2}=3\frac{1}{2}\)

Answer:

\(3\frac{1}{2}\)