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Surface area formula
The formula for surface area is the formula that is used for calculating the surface area for the given 3dimensioanl figure, which occupies the space by its surface. In this article, we will cover the information regarding the formulas for calculating the surface area of different 3-D shapes.
The formula for surface area is mainly used for getting the total submission of surface areas of different 3-D shapes. The formula for calculating surface area is divided into two different categories:
The formula for total surface area
The formula for the curved surface area is also known as the formula for lateral surface area
The chart given below shows the formula for different 3-D object’s surface areas
Object’s name | Formula for | Formula for Total surface area |
Cuboid | 2h(l+h) | 2(hl+ lb+ bh) |
Sphere | 4πr2 | 4π(r2) |
Prism | Height × perimeter of the base | lateral surface area + 2 (area of the base) |
Cylinder | 2πrh | 2πr (r + h) |
Cube | 4a2 | 6a2 |
Hemisphere | 2πr2 | 3πr2 |
Cone | Πrl | Πr (l+ r) |
Pyramid | ½(base perimeter)×height | Area of the base +lateral surface area |
Solved examples of the surface area formula
Example 1: A tank has a cylindrical shape having a radius of 6 yds and a height of 12 yds. With the help of the surface area formula, find it’s the surface area of the cylindrical tank. If the painting cost of the tank is $3 per yd2, determine what will be the cost of painting the tank?
Solution:
As we already know that the formula for the total Surface Area formula of cylinder
= 2πrh + 2πr2
or, 2πr(r + h)
=2 × 22/7 × 4 × (12 + 12)
=603.43 yd2
Cost of painting at $3 per yd2 = 603.48 × 3 = $1810.2857
Hence, The total cost of painting the cylindrical tank is $1810.2857
Example 2: For a given cube with a side length of 7 inches find its surface area by using the formula of the surface area of a cube showing each and every step
Solution: Given
The side length of the cube is 7 inches
The formula for finding the surface area of a cube = 6a2
a = 7 inches
By substituting the values in the formula of the surface area of a cube.
= 6 (7)2
= 6 (49)
= 294 inches2
∴The surface area of a cube will be 294 inches2
