How To Find The Area Of A Sphere Formula

The surface expanse of a sphere is divers equally the region covered by its outer surface in iii-dimensional space. A Sphere is a three-dimensional solid having a circular shape, just like a circumvolve. The formula of full surface expanse of a sphere in terms of pi ( π ) is given by:

Surface expanse = 4 π rⁱⁱ square units

The difference betwixt a sphere and a circle is that a circle is a ii-dimensional figure or a flat shape, whereas, a sphere is a three-dimensional shape. Therefore, the area of circle is dissimilar from area of sphere.

Area of circle = π r²

Definition

From a visual perspective, a sphere has a three-dimensional construction that forms past rotating a disc that is circular with ane of the diagonals.

Allow 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. Nosotros ascertain this term as the total surface expanse.

The surface area of a sphere is equal to the areas of the entire face surrounding it.

Surface Area of a Sphere

Formula

The surface surface area of a sphere formula is given by,

A = four π r^twofoursquare units

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

Curved Surface Area
Lateral Surface Surface area
Total Surface Surface area

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

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

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

In instance of a Sphere, it has no flat surface.

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

Solved Examples

Example 1– Summate the price required to paint a football game which is in the shape of a sphere having a radius of 7 cm. If the painting cost of football is INR two.5/square cm. (Take π = 22/7)

Solution

Nosotros know,

The full surface area of a sphere = 4πr²square units

= 4 × (22/7) × seven × 7

= 616 cm²

Therefore, full toll of painting the container = 2.5 × 616 = Rs. 1540

Exampl due east 2- Calculate the curved area of a sphere having radius equals to 3.five cm(Take π= 22/vii)

Solution –

We know,

Curved area = Total surface area = 4πr²square units

= four × (22/7) × 3.5 × iii.five

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

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Oft Asked Questions – FAQs

What is the surface surface area of sphere?

The surface surface area of a sphere is total area covered past its outer surface in iii dimensional space.

How to discover the expanse of a sphere?

To find the surface surface area of a sphere, we tin can employ the formula:
SA = four π r^two square units
Where r is the radius of sphere

What is the area of hemisphere?

Area of hemisphere is equal to the sum of its curved surface area and base area. The formula is given by: iii π r² square units

What is the surface surface area of a cone?

The surface expanse of cone is the sum of its curved surface area and circular base expanse. The formula is given past:
TSA = πr(l+r)
Where l is the camber heigh of the cone and r is the radius of the circular base.