Volume of a Sphere

Volume of a Sphere

Here we are going to explain about volume of a sphere, surface area of sphere, formulas and solved examples. Check all the details here

Volume of a Sphere

A sphere is a geometrical figure whose set of all points in three-dimensional space are at the same distance (the radius) from a given point (the centre), or the result of rotating a circle about one of its diameters. In order to determine the volume of a sphere, one must apply the formula required to calculate it. The sphere is also the one of the most important topics of geometry that is asked in the government recruitment exams. Generally, there are questions asked are related to basic concepts and formulas. To let you make the most of the Mathematics section

A sphere is a three-dimensional figure in which every point on its surface is equidistant from its center. It has no edges and vertices. Example of spherical figure is football, volleyball, etc. There are two types of sphere namely solid sphere and hollow sphere. The volume of a sphere is defined as the space occupied inside it. The volume of a sphere is the amount of area covered inside the outer surface of a sphere. It is measured in the cubic units m3, cm3, in3, etc.

The volume of the sphere depends on the radius as we take cross-section to calculate the volume and it is a circle. Here we are going to discuss the volume of a sphere, the surface area of a sphere, the formula of volume and surface area of a sphere, etc. So refer to the article to get detailed information about the sphere and its related terms and concepts.

Volume of Sphere = 4/3πr3

Here we are providing the definition, properties, formula with examples of a sphere for the better understanding of students.

Volume of a sphere: Definition

A sphere is a three-dimensional figure in which every point on its surface is equidistant from its center. It has no edges and vertices. Example of sphere is football. The spheres are of two types  namely solid sphere and hollow sphere.

The volume of a sphere is a measure of the region occupied inside the figure. It can simply be defined as the capacity of the sphere. A sphere is obtained on the rotation of a two-dimensional figure circle. The volume of the sphere depends on the radius and it gets increases by increasing the radius and vice-versa. The volume of a sphere is derived here. Refer to the below steps to get the volume of a sphere.

Sphere Surface Area

The surface area of a sphere is defined as the region covered inside the outer surface of a sphere. A sphere is a three-dimensional solid object and its surface area is calculated as

The surface area of the sphere  =  4 π r2 square units

It is a three-dimensional object and the surface area of any 3d object has the following three types:

Curved Surface Area – It is the area of all the surfaces covered by the sphere.

Lateral Surface Area – It is the area of the sphere excluding the area of bases. It is simply the areas of the top and bottom surfaces of the object.

Total Surface Area – This is the total area of surfaces including sides, bases, top, and bottom.

Note: In a sphere, there is no flat surface present so the total area of the sphere = curved surface area of a sphere

Area of Sphere

A sphere is a three-dimensional figure bounded by curved surfaces present equidistant from the center. It is a perfectly round-shaped figure like a football, ball, etc. The distance between the center to the outer surface is termed the radius of the sphere. The area of the sphere is the region occupied by the outer surface in a three-dimensional space. The formula to calculate the area of a sphere is mentioned here.

Area of Sphere = 4π r2 

For a sphere, the area of a sphere, cursed surface area, or the total surface area is the same and calculated using the above formula only.

Sphere Shape

The sphere is a round-shaped three-dimensional figure bounded by curved surfaces. It has no edges and vertices and can be created by the rotation of a two-dimensional circle. Every point on the surface of a sphere is equidistant from the center of the circle which is known by the radius of the circle. You can observe the shape of the sphere by taking an example of the ball or the diagram shown above.

Volume of a Sphere: Formula

Greek philosopher Archimedes discovered The formula for the Volume of a sphere over two thousand years ago. He was the first person to state and prove that the volume of a sphere is exactly two thirds the volume of its circumscribed cylinder, which is the smallest cylinder that can contain the sphere. The spherical object is placed inside a solid container where the radius of the spherical object is equal to the radius of the circular bases of the cylinder. The Diameter of a sphere is equal to the height of the cylinder.

Volume of a sphere= 2/3 volume of a Cylinder

Volume of a Sphere = 2/3 (πr2h); where r is the radius and h is the height of the cylinder

Now we know that height of cylinder= diameter of the sphere

Therefore,

Volume of a Sphere=  2/3 (πr2.2r); Diameter= 2x Radius

Volume of a Sphere= 4/3(πr3)

Volume of a Sphere: Solved Examples

1. Radius of a sphere is 11cm. Calculate its volume

Solution: We are given the radius of the sphere= 11cm

We know that Volume of Sphere= 4/3(πr3)

Volume of sphere= 4/3 (3.14×113)

Volume of sphere= 5572.45 cm3

2. Find the volume of the sphere having a radius of 5cm.

Solution: As we know, the volume of a sphere, V = (4/3)πr3

Given, r = 5cm

Thus, the volume of a sphere, V = (4/3)πr3 = (4/3 × π × 53) cm3

V = 4/3×3.14×125

V = 523.33 cm3

3.What is the amount of air that can be held by a spherical ball of diameter 20 inches?

Solution: We need to find the volume of the ball.

The radius of the ball will be half the diameter = 20/2 inches = 10 inches

Using the volume of sphere formula, the volume of the ball is

Volume of the ball = (4/3)πr3 = (4/3 × 22/7 × 20^3) = 33523.80 in3

∴ The amount of air that can be held by the spherical ball of diameter 20 inches is 33523.80 cubic inches.

4. Find the volume of a sphere whose radius is 8 cm?

Solution: Given, Radius, r = 8 cm

Volume of a sphere = 4/3 πr3 cubic units

V = 4/3 x 3.14 x 83

V = 4/3 x 3.14 x 8 x 8 x 8

V = 2143.573 cm3

5. Find the volume of sphere whose diameter is 12 cm.

Solution: Given, diameter = 12 cm

So, radius = diameter/2 = 12/2 = 6 cm we know the formula of volume of the sphere,

Volume = 4/3 πr3 cubic units

V = 4/3 π 63

V = 4/3 x 22/7 x 6 x 6 x 6

V = 4/3 x 22/7 x 216

V = 905.142 cu. cm.

6. A hollow sphere is designed by a company such that its thickness is 10 cm and 6 m inside diameter. What will be the volume of the sphere designed by the company?

Solution: Given that the inside diameter is 6 m and thickness is 10 cm, equal to 0.1 m.

Therefore, the outer diameter will be 6 + 0.1 m = 6.1 m.

The volume of a hollow sphere is denoted by: Volume = 4/3 ?R3 – 4/3 ?r3, where R is the radius of the outer sphere and r is the radius of the inside sphere.

Putting the values in the above equation, we get,

V = 4/3 ? (3.053 – 33) = 4/3 ? (1.37)

Therefore, V = 5.735 m3.

7. Find the volume of a sphere if its surface area is 100 square meters.

Solution: We know that the surface area of a sphere is given by S = 4?r, where r is the radius of a sphere.

Therefore, S = 4?r = 100

Finding the value of r, we get, r = 7.96 m

The volume of a sphere is given by V = 4/3  ? r3

Putting the value of r, we get,

V = 4/3 ? (7.96)3 = 2111.58 m3.

8. Calculate the cost required to paint a football which is in the shape of a sphere having a radius of 6 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 r2 square units

= 4 × (22/7) × 6 × 6

= 452.16 cm2

Therefore, total cost of painting the container = 2.5×452.16 = 1130.4

9. 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 r2 square units

= 4 × (22/7) × 3.5 × 3.5

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

10. If the radius of a sphere is 20 feet, find its surface area. (Use π = 3.14).

Solution: Given, that the radius ‘r’ of the sphere = 20 feet.

The surface area of the sphere = 4πr2 = 4 × π × 202 = 5024 feet2

∴ The surface area of the sphere is 5024 feet2

Volume of a Sphere- FAQs

Que.1 Define the volume of the sphere?

Ans – The volume of a sphere is the region occupied by the curved surfaces of the sphere in a three-dimensional space.

Que.2 What is the surface area of a sphere?

Ans – The surface area of a sphere is defined as the total area of the outer surfaces of the sphere.

Que.3 What is the difference between a circle and a sphere?

Ans – A circle is a two-dimensional figure while a sphere is s three-dimensional figure. A sphere can be generated by the rotation of a circle.

Que.4 How to calculate the volume of a sphere? Give formula.

Ans – The volume of a sphere can be calculated by the formula 4/3 π r3

where r = radius of the sphere and π = 22/7 or 3.14

Que.5 Give the formula to calculate the surface area of the sphere?

Ans – The formula to calculate the surface area of the sphere there is 4πr^2. Where r is the radius of the sphere and π = 22/7 = 3.14.