Answer:
The volume of the larger solid is [tex]1,798\ ft^{3}[/tex]
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar , then the ratio of its surface areas is equal to the scale factor squared
so
Let
z-------> the scale factor
x-------------> surface area larger solid
y-------------> surface area smaller solid
[tex]z^{2} =\frac{x}{y}[/tex]
substitute
[tex]z^{2} =\frac{1,198}{312}[/tex]
[tex]z=\sqrt{\frac{1,198}{312}}[/tex] ----> scale factor
step 2
Find the volume of the larger solid
we know that
If two figures are similar , then the ratio of its volumes is equal to the scale factor elevated to the cube
so
Let
z-------> the scale factor
x-------------> volume of the larger solid
y-------------> volume of the smaller solid
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=\sqrt{\frac{1,198}{312}}[/tex]
[tex]y=239\ ft^{3}[/tex]
substitute the values
[tex](\sqrt{\frac{1,198}{312}}^{3})=\frac{x}{239}[/tex]
[tex]x=239*(\sqrt{\frac{1,198}{312}}^{3})=1,798\ ft^{3}[/tex]
