Because the two cylinders are similar, you can use a proportion to determine the height of the larger cylinder
\(3/7 = 5/x\)
By solving the proportion, you get a value for x
\(x = 1 \frac23\)
Now, by multiplying the radius of the larger cylinder by the x value we just found, we can find the height of the larger cylinder
\(1 \frac23*7= 11 \frac23\)
Now, just subsitute the newly found height, and width of the cylinder into the surface area equation
\(A = 2 \pi r h + 2 \pi r^2\)
\(A = 2 \pi (5)(11\frac23)+2 \pi(5)^2\)
\(A \approx 523.6\)
The surface area of the larger cylinder is \(\textbf 5 \textbf 2 \textbf 3 \textbf . \textbf 6 \space \textbf m^ \textbf 2\)
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