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 upto 2 digits and enter non-zero and positive values only.
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 = 6a2
"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 = 4πr2
"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 = 3πr2
"r" is the radius, and "π" is a constant
Solved Examples on Surface Area Calculator
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.