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Surface area of a Sphere

In this section, we will learn sphere definition, properties, and area of sphere formula along with examples in detail.

Sphere

A sphere is a round shape solid object in three-dimensional space. It can be defined as the set of points that are all at the same distance form a given point (center). The perfect example of the sphere is the globe and ball.

Surface area of a Sphere

There is a slight difference between a sphere, and a circle is that a circle is a two-dimensional shape while the sphere is a three-dimensional shape.

Hemisphere

It is the half of the sphere.

Surface area of a Sphere

Properties of a Sphere

  • It is symmetrical.
  • It is not a polyhedron shape (a three-dimensional shape with flat polygonal faces, sharp corners).
  • The center has equidistant from all the points on the surface.
  • Its center does not have a surface.
  • Its width and circumference are constant.
  • It has no flat surface.

Surface Area of a Sphere

The region covered by the surface of a sphere is called the surface area of a sphere. The surface area of a sphere is the same as the surface area of a cylinder with the same radius and height as the sphere.

We can also say that it is four times the area of a circle.

Surface Area of a Sphere (A) = 4πr2

The surface area of a sphere in terms of diameter:

Surface Area of a Sphere (A) = πd2

Where d is the diameter.

Surface area of a Sphere

The area of a three-dimensional shape can be divided into three categories:

  • Curved Surface Area: It is the area of all curved regions of the solid shape.
  • Lateral Surface Area: It is the area of all the regions except bases top and bottom.
  • Total Surface Area: It is the area of all the sides (top, bottom, and solid).

From the above points, we can conclude that:

Total surface area of a sphere = Curved Surface area of a Sphere

Surface Area of a Hemisphere

Surface Area of a hemisphere (A) = 2πr2

Examples

Example 1: The radius of a sphere is 4.7 cm. Find the surface area of the sphere.

Solution:

Given, radius (r) = 4.7 cm

We know that,

Surface Area of a Sphere (A) = 4πr2

Putting the value of r in the above formula we get:

A = 4 * 3.14* (4.7)2

A = 4 * 3.14 * 22.09

A = 277.4504 sq. cm.

The surface area of the sphere is 277.4504 sq. cm.

Example 2: Find the surface area of a globe whose radius is 12 cm. Round the answer to the nearest hundredth.

Surface area of a Sphere

Solution:

Given, radius of globe (r) = 12 cm

We know that,

Surface Area of a Sphere (A) = 4πr2

Putting the value of r in the above formula we get:

A = 4 * 3.14* (12)2

A = 4 * 3.14 * 144

A = 1808.64 sq. cm.

The surface area of the sphere is 1808.64 sq. cm.

Example 3: The radius of a hemisphere is 6.6 cm. Find the surface area of the hemisphere without the base.

Solution:

Given, radius of hemisphere (r) = 6.6 cm.

Surface area of a Sphere

We know that,

Surface Area of a hemisphere (A) = 2πr2

Putting the value of r in the above formula, we get:

A = 2 * 3.14 * (6.6)2

A = 2 * 3.14 * 43.56

A = 273.5568 cm2

The surface area of the hemisphere is 273.5568 cm2.

Example 4: Find the surface area of the sphere whose diameter is 7 cm.

Solution:

Given, diameter of the sphere (d) = 7 cm.

Surface area of a Sphere

We know that,

Surface Area of a Sphere (A) = πd2

Putting the value of d in the above formula, we get:

A = 3.14 * (7)2

A = 3.14 *49

A = 153.86 cm2

The surface area of the sphere is 153.86 cm2.






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