Question

Can you please help me out with a question

Answer 1

The surface area of a cylinder is given below

`2\pi r^2\text{ + 2}\pi rh\text{ = 2}\pi r(r+h)`

For similar shapes, The ratio of two areas is equal to the ratio of their two radii squared Mathematically represented thus:

`\begin{gathered} (A_1)/(A_2)=((r_1)/(r_2))^2 \\ \text{Assume terms with subscript 1 are proportions of the smaller area and radii} \\ ((2)/(7))^2=\text{ (}(16\pi)/(A_2)\text{)} \\ (4)/(49)=\text{ }(16\pi)/(A_2) \\ X\text{ multiplying gives } \\ 4A_2=\text{ 784}\pi \\ \text{Dividing both sides by 4} \\ (4A_2)/(4)=(784\pi)/(4) \\ A_2=\text{ 196}\pi \\ A_2=615.75\text{ sq ft} \end{gathered}`

The area of the bigger cylinder is 615.75 sq ft