The ratio of the volume of the small prism to the volume of the large prism is, 3:5
"A prism is three dimensional structure that has two identical shapes facing one another. These identical shapes make up the bases and can be any polygons."
[tex]V=Bh[/tex]
here, V represents the volume of the prism
[tex]B[/tex] represents the base area of the prism
[tex]h[/tex] represents the height of the prism
For given question,
Let for the small prism [tex]V_{1}[/tex] , [tex]B_{1},h_{1}[/tex] represents the volume, base area and the height respectively
Let for the large prism [tex]V_{2},B_{2},h_{2}[/tex] represents the volume, base area and the height respectively
From given data, [tex]h_{1}=12[/tex] ft and [tex]h_{2}=20[/tex] ft
The volume of the small prism is, [tex]V_{1}=12[/tex] × [tex]B_{1}[/tex]
The volume of the large prism is, [tex]V_{2}=20[/tex] × [tex]B_{2}[/tex]
The ratio of the volume of the small prism to the volume of the large prism is,
⇒ [tex]\frac{V_{1}}{V_{2}} =\frac{12B_{1}}{20B_{2}}[/tex]
Since the prisms are similar, their base area is same.
As, [tex]B_{1}=B_{2}[/tex]
⇒ [tex]\frac{V_{1}}{V_{2}}= \frac{12}{20}[/tex]
⇒ [tex]\frac{V_{1}}{V_{2}}=\frac{4\times3}{4\times5}[/tex]
⇒ [tex]\frac{V_{1}}{V_{2}} =\frac{3}{5}[/tex]
Hence, the ratio of the volume of the small prism to the volume of the large prism is 3:5
Learn more about the volume of the prism here:
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