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# Area of Sphere- Formula in Maths

The region covered by a spherical object’s surface in three-dimensional space is known as the area of sphere or total surface area of sphere. The curved surface area of the sphere is equal to the overall area of the sphere because it is a full curved shape. It’s sometimes referred to as lateral surface area.

## Area of Sphere

A sphere is a solid shape that is bordered by a curved surface with every point on the surface being the same distance from the centre. In other terms, a sphere, like the surface of a round ball, is a fully round geometrical entity in three-dimensional space. The radius of a sphere is the distance between its centre and its outside surface. The surface area of a sphere is equal to 4r2 and is defined as the amount of territory covered by the sphere’s surface. The volume of a sphere is the amount of space it takes up in three dimensions.

A sphere is defined mathematically as a collection of points in three-dimensional space that are all at the same distance from a single point.

The radius of the sphere is the distance from the centre to the outermost surface, while the diameter is the line that links two points on the sphere and is twice the radius’s length. ## Area of Sphere is Equal to

area of sphere A is equal to

A = 4πr2

## Properties of a Sphere

The following are some of the most important features of a sphere:

1.      A sphere does not have a face or an edge.

2.      A sphere is symmetrical in every way.

3.      It isn’t a polyhedron at all.

4.      The surface’s points are all equidistant from the sphere’s centre.

5.      It just has one surface.

## Surface Area of Sphere

A sphere is a three-dimensional shape in which the total surface area of the figure is equal to the curved surface area. The curved surface area is the portion of the surface that is only covered by the curved component. The circular base is not taken into consideration in the formula.

The total surface area, on the other hand, is made up of the curved area as well as the base area. The formula for the sphere’s total surface area and curved surface area is given below.

 Surface area (TSA) = CSA = 4πr² square units

## Area of Hemisphere

Hemisphere is a three-dimensional form that is half of a sphere. A hemisphere is formed when a plane divides a spherical into two equal half.

The sum of a hemisphere’s curved surface area and base area is its total surface area (TSA) (circular base).

• Total Sphere Area (hemisphere) = Half of area of sphere + Base area
• TSA = 2πr² + πr²
 TSA = 3πr²

## Area of Sphere: Sample Problems

Problem: Find the sphere of a sphere of diameter 12 m, rounding your answer to two decimal places (using pi = 3.14).

Soln: Diameter of the sphere (d) = 12 m

Finding the radius of the sphere,

• Radius of the sphere (r) = d/2 = 12/2 = 6 m

Area of the sphere (V) = 4 π r2

• V = 4 x 3.14 x 62
• V = 4 x 3.14 x 6 x 6
• V = 452.16

Therefore, the volume of the sphere is 904.32 m3 .

Problem: A plane passes through the centre of a sphere and forms a circle with a radius of 10 feet. What is the surface area of the sphere?

Soln: Radius of the sphere = 10 feet

Area of Sphere (A) = 4 π r2

• Area = 4 x 3.14 x 10 x 10
• Area = 1256

Therefore, area of the sphere is 1256 feet2.

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## Area of Sphere: FAQs

Q. What is the area and volume of a sphere?

Ans. A sphere with radius r has a volume of 4/3 πr3square unitsand a surface area of 4πr² square units. A sphere has several interesting properties, one of which is that, of all shapes with the same surface area, the sphere has the largest volume.

Q. What is diameter of sphere?

Ans. The largest distance between two antipodal points on the surface of a sphere is its diameter. If is a circle’s or sphere’s radius, then. The circumference of a circle or the great circle of a sphere divided by its diameter.

Q. What is Curved Surface Area and Total Surface Area of sphere and hemisphere?

Ans. Sphere: Surface area (Total Surface Area) = Curved Surface Area = 4πr2.

Hemisphere: Curved surface area (CSA) = 2 π r2.

Total surface area = TSA = 3 π r2.

Q. Why is a sphere 2/3 of a cylinder?

Ans. A sphere’s volume V is four-thirds of pi times the radius cubed. A hemisphere’s volume is half of the volume of the associated sphere. A sphere’s volume is 2/3 that of a cylinder with the same radius and height equal to the diameter.

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