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
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