Question

calculator
a prism is dilated by a factor of 1.5.
how many times larger is the volume of the resulting prism than the volume of the original prism?
enter your answer as a decimal in the box

Explanation:

Step1: Recall the volume - dilation formula

If a three - dimensional object is dilated by a scale factor \(k\), the ratio of the volume of the dilated object \(V_{new}\) to the volume of the original object \(V_{old}\) is given by \(V_{new}/V_{old}=k^{3}\). Here, the scale factor \(k = 1.5\).

Step2: Calculate \(k^{3}\)

Substitute \(k = 1.5\) into the formula \(k^{3}\). Using the formula \(a^{3}=a\times a\times a\), we have \(1.5\times1.5\times1.5=(1 + 0.5)\times(1 + 0.5)\times(1 + 0.5)\). First, \(1.5\times1.5=2.25\), then \(2.25\times1.5=(2+0.25)\times1.5=2\times1.5 + 0.25\times1.5=3+0.375 = 3.375\).

Answer:

\(3.375\)