# Surface Area and Volume of a Cylinder

Hi, when I recently went to a coffee shop, I saw a hike in price. I wondered and asked the shop owner about it, he said it’s because the mug size is big. You must be wondering how an increase in size affects the price? Have you ever thought of finding the __surface area of a cylindrical__ coffee mug? Do you know what a cylinder is? What is a three-dimensional shape?

Well! Here is the answer to all your questions.

## Surface Area of the Cylinder

A Cylinder has a circular top, bottom, and a curved surface in between. Ex: Battery shell, tin can, etc. The surface area of a cylinder is a sum of all three areas.

Surface Area of the Cylinder = Area of circular bottom + Area of top circle + Area of the curved face.

You know that the area of the circle = πr^{2 }

Area of curved surface = 2πr

So, Surface area of the cylinder = πr^{2} + 2πrh + πr^{2} = 2πr^{2} + 2πrh

Now, we can take out 2πr as common

Hence, Surface area of the cylinder = 2πr(r + h)

Isn’t it easy? This surface area calculation is handy while performing various activities. For instance, to calculate the amount of paint required while painting cylindrical structures like pillars.

## Volume of the Cylinder

Volume is nothing but the quantity of space that can be filled by anything. The volume of a cylinder is highly beneficial in our daily life. For example, designing syrup measuring cups, designing perfume bottles, etc. Now you must be keen to find the __volume of cylinder__. For this, you must know the basic rule for finding the volume of all the three-dimensional shapes. That is, the volume of any three-dimensional shape is equal to the product of area and height.

- The volume of the Cylinder = Area of its base × Height
- Area of the base = πr
^{2 }Height = h - The volume of the Cylinder = πr
^{2}h

## Other Shapes Like Cylinders:

Can we calculate the volume for all the shapes? No. Volume is calculated only for 3-dimensional shapes. Let us discuss the shapes in detail now. Shapes are of three categories.

- One-dimensional shape
- Two-dimensional shape
- Three-dimensional shape

- One dimensional shape: These shapes have only length.

Ex: Straight line

- Two-dimensional shape: These shapes have length and breadth.

Ex: rectangle, square, etc.

- Three-dimensional shape: These shapes have length, breadth, and depth.

Everything which you see in your surroundings is three-dimensional.

Ex: Stone, frame, building, etc.

As we discussed earlier Volume is the quantity of space that can be filled by a solid, liquid, or gas. So to fill something the shape must have length, breadth, and depth. Hence we can calculate volume only for 3-dimensional shapes.

## Illustration

Let us take the radius of the mug as 2 cm, Depth as 6cm.

Surface area of Cylinder = 2πr(r + h) = 2 × π × 2 (2 + 6)

Surface area of Cylinder = 32π cm^{2}

Volume of the cylinder = πr^{2}h = π × 4 × 6

Volume of the cylinder = 24π

But now the new radius of the mug is 3 cm and height is 6 cm.

∴ New Surface area of cylinder = 2πr(r + h) = 2 × π × 3 (3 + 6)

New Surface area of cylinder = 54π cm^{2}

Volume of the cylinder = πr^{2}h = π × 9 × 6

Volume of the cylinder = 54π

So, the vendor was right.

An increase in the size of the mug increases the volume. Hence the quantity of coffee has increased and so is the price. We learned so many things about the cylinders. Thanks to the coffee vendor who motivated us to learn so many new things.

Does the thickness of the cylinder have anything to do with area and volume? Try to find the answer to this using Cuemath, which makes maths easier to understand.