Answer:
The area of a cover that will fit on the larger tank is 6 square inches
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its Volumes is equal to the scale factor cubed
Let
z ---> the scale factor
so
[tex]z^3=\frac{64}{8}=8[/tex]
[tex]z=2[/tex]
step 2
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z ---> the scale factor
x ---> the area of a cover that will fit on the larger tank
y ---> the area of a cover that will fit on the smaller tank
so
[tex]z^2=\frac{x}{y}[/tex]
we have
[tex]z=2\\y=1.5\ ft^2[/tex]
substitute the given values
[tex]2^2=\frac{x}{1.5}[/tex]
solve for x
[tex]x=4(1.5)=6\ ft^2[/tex]
