# Surface Area of a Cylinder Calculator

**Surface Area of Cylinder -**The Surface Area of a Cylinder is equal to the sum of the areas of the bases each having an area of π ⋅ r2 , plus the area of the side. The area of the side is equal to the area of a rectangle with length 2 π r (the circumference of the base) times the height.

### What is meant by Surface Area of a Cylinder?

The surface area of the cylinder is the summation of the areas of two congruent circles and a rectangle. The area of this rectangle is the lateral area of the cylinder. It is obvious that the length of the rectangle is equal to the circumference of the base. Hence, the lateral area of the cylinder is **L=2rπ×h**, where π ≈ 3.14.

Finally, to find the surface area of a cylinder, first, calculate the lateral area and then compute the areas of base circles by summation. The formula for the surface area of a right cylinder is **A = 2πrh + 2(πr2) = 2πr(h+r).**

### Surface Area of a Cylinder Formula

The total surface area of a closed cylinder Formula is:

- A = L + T + B = 2πrh + 2(πr2) = 2πr(h+r).

The lateral surface area of a cylinder (just the curved outside):

- L = 2πrh

The top and bottom surface area of a cylinder (2 circles):

- T = B = πr2

### How to Find Surface Area of a Cylinder?

To calculate the Surface Area of a Cylinder, first, you should break it down into three parts in your imagination. The three parts can be represented as,

- The two circles that make up the ends of the cylinder.
- The side of the cylinder, which when "unrolled" is a rectangle.

Hence, the base surface area of a cylinder equals two times the area of a circle with the radius r, and the lateral surface area of a cylinder is equal to the area of a rectangle. The first side of this rectangle is the height of the cylinder h and the second is the circumference of the base ie., 2 * π * r.

Thus, the lateral surface area of a cylinder is 2 * π * r * h.

Now, you need to calculate the base surface area, so you must compute the area of a circle with the radius r and multiply it two because that every cylinder has two bases.

Thus, the base area of a cylinder is 2 * π * r2.

Finally, the formula of the total surface area of the cylinder is the sum of the base surface area and the lateral surface area ie.,

Total Surface Area of a Cylinder = base area + lateral area,

A = 2 * π * r² + (2 * π * r) * h,

**A = 2 * π * r * (r + h)**

That's it, now you had an output of the Surface Area of a Cylinder after substituting the values in base radius and height.

**Example**

Find the Surface Area of a Cylinder when the radius is 12 cm and height is 6 cm?

**Solution:**

Given that Base radius(r) = 12 cm, and

Height(h) = 6 cm

Substitute the values in the formula of the **Surface Area of Cylinder = 2π * (Radius)2 + 2π * (Radius) * (Height)**

where Pi (π) is approximately equal to **3.14.**

On simplifying further we get as such A= 2 (π) * (122) cm2 + 2 (π) * (12) cm * (6.0) cm

⇒Raise 12.0 cm to the power of 2.

2(π) * (144.0) cm2 + 2 (π) * (12.0) cm * (6.0) cm

⇒ Multiply 144.0 cm2 by 2

288.0 cm2 π + 2(π) * 12.0 cm * 6.0 cm

⇒ Multiply 12.0 cm and 6.0 cm

288.0 cm π + 72.0 cm2 π * 2

⇒ Multiply 72.0 cm2 and 2

288.0 cm2 . π + 144.0 cm2 . π

⇒ Add 288.0 π cm2 and 144.0 π cm2

The result can be shown in multiple forms as 432.0 π cm2

Thus, Surface Area of Cylinder whose radius and height are 12.0 cm & 6.0 cm is **432.0 π cm2**

If you solve it in a Decimal Form the Surface Area of Cylinder 12.0 cm by 6.0 cm is** 1356.48 cm2**

### How to Use Surface Area of Cylinder Calculator?

Students can easily use our **Surface Area of a Cylinder Calculator** because it is a very handy and free online tool. By using our handy calculator you can make your calculations like how to find the Surface Area of a Cylinder faster. So, follow the below steps and know how to use this free online Surface Area of Cylinder Calculator:

- First, give your parameters like base radius and heights as inputs in the appeared fields.
- Now, choose the given metric for each input in cm, m, ft, yd, mi, etc. by clicking on them in the dropdown list.
- Then, tap on the Area Button located below to the input fields.
- At last, you will get your Surface Area of a Cylinder as an Output along with a detailed solution.

### FAQs on Surface Area Calculator for Cylinder

**1. What is the Surface Area of a Cylinder (closed) & Formula?**

The surface area of a closed cylinder can be calculated by summing the total areas of its base and lateral surface:

- base SA = 2πr2,
- lateral SA = 2πrh,
- Total Surface Area of a Cylinder = 2πr(r + h) where 'r' is radius and 'h' is height

**2. How do you find the surface area of a closed cylinder?**

You can find the surface area of a cylinder using our free online & handy calculator and get the output in a fraction of seconds.

**3. What is the surface area of a cylinder with the base radius r = 3 cm and the height h = 5 cm?**

After substituting the given parameters into the formulas, the base surface area is 56.55 cm² and the lateral surface area is 94.25 cm². Now substitute the two values in the formula of the total surface area and then the output of the cylinder surface area is 150.8 cm2.

**4. What is the Surface Area of a Cylinder Calculator?**

The Surface Area of a Cylinder Calculator is a free online tool that displays the cylinder surface area in a given unit metric.