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Q.

The formula for TSA of cylinder:[[1]]

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Detailed Solution

Assume a cylinder of base radius r and height h as follows
Question Image

Question Image

We know that the base and apex of a cylinder is a circle.
We know that the formula for the circumference of a circle of radius r is given as
C=2πr
We also know that the formula for the content of a circle of radius r is given as
A =

π r^{2}

Now we will find the total surface area of the cylinder.
We know that the formula for the total surface area for any figure is given as
TSA= (height)(base circumference)+(base area)+(top area)
Here we see that the base and top of the cylinder is a circle.
Assume that the total surface area of the cylinder is TSA
Now, using the above formula, we get the total surface area of any image on a cylinder
⇒TSA = (h)(2πr) + (

π r^{2}

)+(

π r^{2}

)
⇒TSA = 2πrh +

2 π r^{2}

Therefore, we can conclude that the total surface area of the cylinder is given as
TSA = 2πrh +

2 π r^{2}

Where, r is the base radius of the cylinder and h is the height of the cylinder.

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