Question

a rectangular prism is 5 meters by 8 meters by 7 meters. the side that is 7 meters long is doubled, the other sides lengths are unchanged. how does the volume change? the volume is 8 times as large; the volume is twice as large; the volume is 7 times as large; the volume is 14 times as large

Explanation:

Step1: Recall volume formula for rectangular prism

The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), where \( l \), \( w \), and \( h \) are the length, width, and height respectively. For the original prism, \( l = 5 \) m, \( w = 8 \) m, \( h = 7 \) m. So original volume \( V_1 = 5\times8\times7 \).

Step2: Calculate new volume

The side of length 7 m is doubled, so the new height \( h_2 = 2\times7 = 14 \) m. The other sides remain unchanged, so new volume \( V_2 = 5\times8\times14 \).

Step3: Find the ratio of new volume to original volume

\( \frac{V_2}{V_1}=\frac{5\times8\times14}{5\times8\times7} \). The \( 5\times8 \) terms cancel out, leaving \( \frac{14}{7}=2 \). So \( V_2 = 2\times V_1 \), meaning the volume is twice as large.

Answer:

The volume is twice as large (Option: The volume is twice as large)