Question

a square prism has base side lengths measuring 4 yards and a height of 12 yards. if the square prism is dilated by a scale factor of k = 2, what is the new volume? 768 yd³ 1,536 yd³ 384 yd³ 192 yd³

Explanation:

Step1: Find original volume formula

The volume formula for a square - prism is $V = s^{2}h$, where $s$ is the side - length of the base and $h$ is the height.

Step2: Calculate original volume

Given $s = 4$ yards and $h = 12$ yards, the original volume $V_{1}=4^{2}\times12=16\times12 = 192$ $yd^{3}$.

Step3: Determine new dimensions after dilation

When dilated by a scale factor $k = 2$, the new side - length of the base $s_{2}=k\times s=2\times4 = 8$ yards and the new height $h_{2}=k\times h=2\times12 = 24$ yards.

Step4: Calculate new volume

The new volume $V_{2}=s_{2}^{2}h_{2}=8^{2}\times24=64\times24 = 1536$ $yd^{3}$.

Answer:

1,536 $yd^{3}$