A three-dimensional shape is a solid shape with height or depth. For example, the sphere, cuboid, sphere, etc. are three-dimensional. The surface area of a three-dimensional shape is the sum total of all of the surface areas of each of the sides. Children will like to think of the shape as a birthday present and the surface area as the wrapping gift paper. If we carefully took the wrapping paper to cover up the gift item, then we have to add the area of all the sides. The total value will be the surface area of the shape. In this article, we will explore the surface area formula of various objects with different shapes. Let us learn the interesting concept!

Source: en.wikipedia.org

**Surface Area Formula**

**What is Surface Area?**

When we are finding the surface area of a 3-D shape, think of it as unfolding the shape, or flattening it out, and then finding the area of each side. When we add all of these areas up, we have the surface area. In order to find the area of a 3-D shape, we must know how to find the area of the basic shapes that make up the sides of the 3-D shape.

For a solid object, the space covered from all sides is termed as the surface area of the object. By measuring surface area we can measure the area of material required to cover the 3-D object completely. Since it is computation of the area, therefore its unit is a square meter or square centimeter or likewise. Computation of the surface area depends upon the shape and size.

**Various Surface Area Formulae:**

The volume of different objects with different sizes and shapes will be calculated as follows:

**Surface Area of a cuboid:**

S =2 × (LB + BH + HL)

Where,

S | Surface Area of Cuboid |

L | Length of Cuboid |

B | Breadth of Cuboid |

H | Height of Cuboid |

**Surface Area of a cube:**

S = 6 × A²

Where,

S | Surface Area of Cube |

A | Side of Cube |

**Surface Area of a Cylinder is:**

\(S=2\pi \times R \times (R+H)\)

Where,

S | Surface Area of Cylinder |

R | The radius of Circular Base |

H | Height of Cylinder |

**Surface Area of a Sphere is:**

\(S =4\pi \times R^2 \)

Where,

S | Surface Area of Sphere |

R | Radius of Sphere |

**Surface Area of a Right circular cone:**

\(S = \pi \times r(l+r) \)

Where,

S | Surface Area of Cone |

R | The radius of Circular Base |

L | Slant Height of Cone |

**Surface Area of a Hemisphere:**

\(S = 3\pi \times R^2 \)

Where,

S | Surface Area of Sphere |

R | Radius of Sphere |

## Solved Examples

Example-1: The dimensions of a rectangular box are given as 5m, 3m and 2m. This tank has to be covered from all sides by cloth. Compute the cost for covering it, if rate of cloth is Rs. 25 per square meter.

Solution:

As given the dimensions of the box in cuboid shape is,

L= 5m

B= 3m

H= 2m

Now, we have to compute the surface area by using formula as:

\(S= 2\time (LB+BH+HL) \)

Putting values,

\(S = 2\times (5\times3 + 3\times 2 + 2\times 5)\)

\(S = 2 \times (15 + 6+ 10)\)

\(S= 62 \; Square Meter\)

So, cost to cover it will be,

\(Cost = S \times Rs. 25\)

\(Cost = 62 \times 25\)

Cost = Rs. 1550

Hence the cost to cover is Rs. 1600.

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