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These cylinders are similar. Find the surfacearea of the smaller cylinder. Round to thenearest tenth.5 cm3 cmSurface Area = [ ? ) cmSurface Area = 236 cm2

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Let me draw the situation here below:

Ok, so:

If both cylinders are similar, that means that there's a relation between each other.

Now, the surface area of a cylinder can be found using the next equation:

Surface area = 2πr² + 2πrh.

Where r is the radius, and h is the height.

Notice that we have the surface area for the big cylinder, so, first, we're going to find its radius like this:

236 = 2πr² + 2πr(5)

236 = 2πr² + 10πr

2πr² + 10πr - 236 = 0. Here we have a quadratic equation!

If we solve this quadratic equation, we obtain that r = 4,11896 approximately.

Now, we have to establish a relation between two cylinders.

We have a relation because two figures are similar. So,

5/4.11896 = 3/r

Finding r, we obtain that r (radius of the small cylinder) is r = 2,471376 approximately.

And finally, we calculate the surface area:

Surface area = 2πr² + 2πrh.

SA = 2π(2,471376)² + 2π(2,471376)(3)

Therefore, SA = 84,96. Rounded to the nearest tenth: SA = 85cm²

These cylinders are similar. Find the surfacearea of the smaller cylinder. Round to-example-1
These cylinders are similar. Find the surfacearea of the smaller cylinder. Round to-example-2
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