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Answer:
The dimensions of the larger cylinder are 3 times the dimensions of the smaller cylinder
The surface area of the larger cylinder is 3^2. or 9 times the surface area of the smaller cylinder
If proportional dimensional changes are made to a solid figure, then the surface area will change by the square of the scale factor of similar solids
Step-by-step explanation:
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 the base of larger cylinder
y ---> the area of the base of smaller cylinder
so
we have
substitute
solve for z
<u><em>Verify each statement</em></u>
1) The dimensions of the larger cylinder are 3 times the dimensions of the smaller cylinder
The statement is true
Because the scale factor is equal to 3 ( see the explanation)
2) The surface area of the larger cylinder is 3^2. or 9 times the surface area of the smaller cylinder
The statement is true
Because, the surface area of the larger cylinder is equal to the surface area of the smaller cylinder multiplied by the scale factor squared
3) If proportional dimensional changes are made to a solid figure, then the surface area will change by the square of the scale factor of similar solids
The statement is true
because
If two figures are similar, then the ratio of its areas is equal to the scale factor squared