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Sagot :
The surface area of a cylinder is given below
[tex]2\pi r^2\text{ + 2}\pi rh\text{ = 2}\pi r(r+h)[/tex]For similar shapes, The ratio of two areas is equal to the ratio of their two radii squared Mathematically represented thus:
[tex]\begin{gathered} \frac{A_1}{A_2}=(\frac{r_1}{r_2})^2 \\ \text{Assume terms with subscript 1 are proportions of the smaller area and radii} \\ (\frac{2}{7})^2=\text{ (}\frac{16\pi}{A_2}\text{)} \\ \frac{4}{49}=\text{ }\frac{16\pi}{A_2} \\ X\text{ multiplying gives } \\ 4A_2=\text{ 784}\pi \\ \text{Dividing both sides by 4} \\ \frac{4A_2}{4}=\frac{784\pi}{4} \\ A_2=\text{ 196}\pi \\ A_2=615.75\text{ sq ft} \end{gathered}[/tex]The area of the bigger cylinder is 615.75 sq ft
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