Surface Area of a Sphere

Surface Area of a Sphere Definition

The surface area of a sphere is defined as the amount of region covered by the surface of a sphere.  A Sphere is a three-dimensional solid object having a round structure, just like a circle. The difference between a sphere and a circle is that a circle is in 2-dimension, whereas, a sphere is a 3-dimensional shape.

From a visual perspective, it has a three-dimensional structure that forms by rotating a disc that is circular with one of the diagonals. Let us consider an instance where spherical ball faces are painted. To paint the whole surface, the paint quantity required has to be known beforehand. Hence the area of every face has to be known to calculate the paint quantity for painting the same. We define this term as the total surface area. The surface area of a sphere is equal to the areas of the entire face surrounding it.

Surface Area of a Sphere

Surface Area of a Sphere Formula

The surface area of a sphere formula is given  by,

A = 4 π rsquare units

For any three-dimensional shapes, the area of the object can be categorised into three types. They are

  • Curved Surface Area
  • Lateral Surface Area
  • Total Surface Area

Curved Surface Area: The curved surface area is the area of all the curved regions of the solid

Lateral Surface Area: The lateral surface area is the area of all the regions except bases(i.e., top and bottom)

Total Surface Area: The total surface area is the area of all the sides, top and bottom the solid object.

In case of a Sphere, it has no flat surface

Therefore the Total surface area of a sphere = Curved surface area of a sphere

Surface Area of a Sphere Example Problems

Example 1 Calculate the cost required to paint a football which is in the shape of a sphere having a radius of 7 cm. If the painting cost of football is INR 2.5/square cm. (Take π = 22/7)

Solution

 We know,

The total surface area of a sphere =  4 π rsquare units

= 4 × (22/7) × 7 × 7

= 616 cm2

Therefore, total cost of painting the container = 2.5 × 616 = Rs. 1540

Example 2- Calculate the curved surface area of a sphere having radius equals to 3.5 cm(Take π= 22/7)

Solution

We know,

Curved surface area = Total surface area = 4 π rsquare units

= 4 × (22/7) × 3.5 × 3.5

Therefore, the curved surface area of a sphere= 154 cm2

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Practise This Question

The diameters of two cones are equal. If their slant heights are in the ratio 5:4, the ratio of their curved surface areas is

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