Question

a triangular pyramid with a volume of 32 in³ is dilated with a scale factor of k = 1.75. what is the new volume? 24 in³ 56 in³ 98 in³ 171.5 in³

Explanation:

Step1: Recall volume - dilation formula

When a three - dimensional figure is dilated by a scale factor \(k\), the new volume \(V_{new}\) is related to the original volume \(V_{old}\) by the formula \(V_{new}=k^{3}V_{old}\).

Step2: Substitute given values

We know that \(V_{old} = 32\mathrm{in}^{3}\) and \(k = 1.75\). So \(V_{new}=(1.75)^{3}\times32\). First, calculate \((1.75)^{3}=1.75\times1.75\times1.75 = 5.359375\). Then \(V_{new}=5.359375\times32\).

Step3: Perform multiplication

\(5.359375\times32 = 171.5\mathrm{in}^{3}\).

Answer:

171.5 in³