# Surface Area Calculator

Surface Area Calculator is an online tool that calculates the total surface area of the specified three-dimensional figure. The complete area of all the surfaces of a 3D object is given by the total surface area.

## What is a Surface Area Calculator?

Surface Area Calculator determines the total surface area of the chosen three-dimensional figure. An object can have two types of surface areas. These are the total surface area and the curved or lateral surface area. To use the * surface area calculator*, enter the values in the input boxes.

### Surface Area Calculator

Note: Enter numbers up to 2 digits

## How to Use the Surface Area Calculator?

Follow the given steps to determine the surface area of the chosen three-dimensional figure using the surface area calculator:

**Step 1:**Go to Cuemath's online surface area calculator**Step 2:**Select the three-dimensional figure from the drop-down list. Enter the values in the input boxes.**Step 3:**Click on**"Calculate"**to find the surface area.**Step 4:**Click on '**Reset**' to clear the fields and enter new values.

## How Does Surface Area Calculator Work?

Given below are the formulas to calculate the surface areas of various objects.

1. Cube

The complete surface area covered by the 6 faces of a cube is known as the total surface area. Each face of a cube is in the shape of a square. Thus, the surface area is given as

TSA of cube = 6a^{2}

"a" is the side length.

2. Cuboid

A cuboid has 6 faces that are rectangular in shape. Thus, we sum up the area of all the 6 rectangular faces to get the total surface area of a cuboid.

TSA of cuboid = 2 (lw + wh + lh)

"l" is the length, "w" is the width and "h" is the height.

3. Cylinder

A cylinder is a solid shape made up of two circular bases that are connected by a curved surface. The formula is given as follows:

TSA of cylinder = 2πr(h + r)

"r" is the radius of the circular base, "h" is the height of the cone, and "π" is a constant that has a value of either 3.14 or 22/7.

4. Cone

A cone has a circular base and tapers smoothly to a point on top that is known as the vertex or the apex. We can calculate the surface area by the formula given below:

TSA of cone = πr(r + l)

"r" is the radius, "π" is a constant and "l" is the slant height.

5. Sphere

A sphere is a 3-D shape that has a round structure like that of a ball.

TSA of sphere = 4πr^{2}

"r" is the radius, and "π" is a constant

6. Hemisphere

When a sphere is cut into two equal halves by a plane passing through its center, then the shape so formed is known as a hemisphere.

TSA of hemisphere = 3πr^{2}

"r" is the radius, and "π" is a constant

## Solved Examples on Surface Area

**Example 1:** Find the total surface area of a cuboid that has the dimensions l = 5.2 units, w = 3.1 units, and h = 7.6 units. Verify the result using the online surface area calculator.

**Solution:**

l = 5.2 units, w = 3.1 units, and h = 7.6 units

TSA of cuboid = 2 (lw + wh + lh)

= 2 (5.2 × 3.1 + 3.1 × 7.6 + 5.2 × 7.6)

= 158.4 square units.

**Example 2:** Find the total surface area of a cone that has the dimensions l = 12.5 units and r = 3 units. Verify the result using the online surface area calculator.

**Solution:**

l = 12.5 units, and r = 3 units.

TSA of cone = πr(r + l)

= π × 3 (3 + 12.5)

= 146.01 square units.

Now, try the surface area calculator to find the total surface area of the following figures.

- A cube with each side of 12 units.
- A hemisphere with a radius of 9 units.

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