The measurement of a space a sphere can occupy is known as the volume of a sphere. A three-dimensional space that has no edges and vertices is known as a sphere. Do you know the volume of sphere formula? No? Let me tell you. Volume of the sphere formula is 4/3 π r.r.r. In this article, we will try to understand the derivation of the formula for volume of the sphere, the different types of spheres, and their formulae. Once you understand what the volume of the sphere formula is, you will be able to solve any question from the volume of the sphere. Let us also understand and learn something about the volume of a cone too.
Volume of a Cone
You definitely have eaten ice cream or seen a Christmas tree. Have you wondered about the size of these objects? These objects are cone-shaped. The amount of space that is occupied by a cone is known as the volume of a cone. A circular base which is made up of radius ‘r’ and diameter ‘d’ is known as a cone. Like all three-dimensional shapes, we will learn about the volume of the cone in detail as well. Stay tuned to know about its formula and how to apply it using some solved examples.
Formula for Volume of a Cone
If the height of the cone is (h) and the radius of the base of the cone is ‘r’ then, the formula for the volume of a cone is given as, 1/3 π r. r h, where r is the radius and h is the height of the cone. The volume of the cone having radius ‘r’ is equal to the volume of the hemisphere having radius ‘r’. We can also calculate the volume of a cone using the diameter and then divide it by 2.
How to Apply the Formula for Volume of Cone
There are three steps through which you can calculate the volume of cones in a given question. Follow the steps given below:
Step 1: Write down the measurements of the radius of the cone ‘r’, the height of the cone ‘h’, and ensure that those measurements are in the same units.
Step 2: After writing down the measurements, place them in the formula of volume of a cone, 1/3πr. rh.
Step 3: Write down the answer in the cubic units.
Let us take an example,
- We will see how to calculate the volume of a cone given that the height of the cone is 1 inch and the radius of the cone is 2 inches.
- Radius of cone = 2 inches
- Height of cone = 1 inch
- Now, using the formula 1/3πr.rh. we get,
- 1/3 × 22/7 × 2 × 2 × 1= 4.1448 cubic inches.
Different Types of Spheres and Their Formulae
- Hollow sphere: Given that, the radius of the inner sphere is ‘r’ and the radius of the outer sphere is ‘R’, the Volume of the hollow sphere is Volume of the outer sphere – Volume of the inner sphere. Mathematically the formula for volume of a hollow sphere is: 4/3 π (R.R.R-r.r.r)
- Solid sphere: We already discussed solid spheres above. Given that, the radius of the sphere is ‘r’ and the volume of a sphere is ‘V’, the formula for volume of a sphere is 4/3 π.r.r.r
Let us take an example.
- We will see how to calculate the volume of a sphere, given that the radius of the sphere is 1 inch.
- Given that, the radius of the sphere is = 1 inch
- Using the formula for volume of a sphere 4/3πr.r.r we get,
4/3 × 3.14 × 1 × 1 × 1= 4.082 cubic inches.
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