March 16 2023

# Sphere – Definition, Sphere Vs Circle, Volume and Surface Area of Sphere

A 3-dimensional geometrical figure that has no vertices and edges is called a sphere. The distance between all the points on the surface of the sphere is equidistant from a point called r which is its center. There are numerous real-life examples of spheres namely, football, tennis ball, moon, eyeball, orange, marbles, and so on. Learning to calculate the volume of a sphere and its surface area of a sphere. In this module, we will go through the formula to calculate the volume of a sphere and also learn how to calculate its surface area. We will also solve sum examples related to both the topics so that the concepts become clearer to you.

## What Do You Mean by the Surface Area of a Sphere?

The total area occupied by the sphere is known as the surface area of the sphere. One important thing to note about the surface area of a sphere is that it is always measured in square units. Archimedes discovered that the surface area of a sphere is equal to the lateral surface area of a cylinder. We know that the formula for the calculation of lateral surface area of cylinder is 2rh where h is the height of the cylinder and r is the radius of the cylinder. In the case of a sphere, its diameter will be equal to the height of the cylinder. Thus the formula of the surface area of a sphere = 4rr square units. It can also be written as 4(d/2)(d/2) where d is the diameter of the sphere.

## What Do You Mean by the Volume of a Sphere?

The amount of space that is contained within a sphere is known as the volume of a sphere. An important thing to note about the volume of a sphere is that it is always measured in cubic units. Archimedes discovered that if the radius of a cylinder, a cone, and a sphere is the same and they have equal cross-sectional area, then their volumes are in the ratio- 1:2:3. The formula for the volume of a sphere can be given as: 4/3 rrr.

## Difference Between a Circle and a Sphere

A circle is a geometrical figure in two-dimensional space while a sphere is a geometrical figure in three-dimensional space. Examples of a circle are compact disks, dinner plates, etc. Examples of a sphere are football, tennis ball, orange, etc.

## Solved Examples of Volume and Surface Area of a Sphere

1. Find the volume of a football that has a radius of 10cm.

Solution: We know that the shape of a football resembles the shape of a sphere. The formula of the volume of a sphere is given as: 4/3 rrr

Thus, volume of the football = 4/3 (10) (10) (10) = 4186.66 cubic cm.

2. You are required to determine the cost to paint a spherical object which has a radius of 8 cm. It is given that the cost of painting is Rupees 3 per square cm.

Solution: To determine the cost of painting, we need to find the surface area of the spherical object.

The formula of the surface area of the sphere is given as: 4rr square units.

Thus, the surface area of the given cylindrical object is = 4 * 22/7 * 8 * 8 = 804.57 square cm.

Cost of painting 1 square cm = Rupees 3

Therefore, Cost of painting 804.57 square cm = 804.57 * 3 = Rupees 2,413.714

If you want to learn more about the concepts of volume of a sphere and its surface area in detail and in a fun and interesting manner, visit Cuemath and learn and understand the Cuemath way.

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