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In our day-to-day life, we come across situations where we have to handle cylindrical objects such as water tanks, cylindrical containers etc. In order to handle these objects, we need to know about the volume of a cylinder. This can help us to calculate the designing of cylindrical objects of larger volume or smaller volume. We can easily find out the volume of a cylinder if we have the height and radius of the object. The volume of a cylinder is the capacity of the cylinder which calculates the material quantity it can contain. Formula for volume of cylinder is πr.rh where r denotes the radius of the cylinder and h denotes its height. Let us now learn how to calculate the volume of a cylinder along with the volume of a sphere.
How to Apply the Formula for Volume of a Cylinder?
The following points shows how to apply the steps to calculate the volume of a cylinder:
Step 1. Make sure that you find out the height ‘h’ and radius ‘r’ of the cylinder of the same units.
Step 2. Now, substitute the values in the formula of volume of cylinder that is πr.rh
Step 3. After calculating the answer, write in cubic units
Let us take an example to solve a question about volume of a cylinder:
We will calculate the volume of the cylinder provided that, height is 1 cm and radius is 4 cm.
Solution:
Given that,
Radius= 4cm
Height= 1 cm
By putting the formula for volume of the cylinder, we get = π × 4 × 4 × 1 = 50.24.
Thus, the volume of the cylinder = 50.24 cubic cm.
If you want to learn more about these concepts in detail and in an interactive and a fun way, visit Cuemath.
Volume of a Sphere
The measurement of the space a sphere can occupy is known as the volume of the sphere. A three-dimensional space that has no edges or vertices is considered as a sphere. Let us take a sheet of paper and draw a circle on it, after drawing a circle take a disc and paste a string along its diameter and rotate it along the strings. This will give you the shape of a sphere. In this short lesson, we will try to find out the formula of volume of the sphere, how to apply the formula and see some examples. Once you understand these points, you can solve any questions regarding volume of the sphere.
Formula for Volume of a Sphere
If the radius of cylinder, cone and sphere is ‘r’ then their volume is in the ratio of 1:2:3. This law was suggested by Archimedes. The formula for the volume of a sphere can be given as a solid as well as the hollow of a sphere. In the case of the solid sphere we only have one radius but for a hollow sphere, there are two radii, having two different values, one for the outer sphere and other for the inner sphere. The common formula of the volume of a sphere is ‘4/3 π r.r.r’. Here, r is the radius of the sphere. This formula is often used if the other 2 are not mentioned.
How to Apply the Formula for Volume of Sphere
We can calculate the volume of the sphere with the following steps given below. There are four steps by which we can calculate the problems of volume of sphere:
Step 1. Check the value of the radius of the sphere.
Step 2. Now, take the cube of the radius of the sphere.
Step 3. Multiply the r.r.r by 4/3 π.
Step 4. At last, add the units to the final answer that is cubic units.
Let us take an example to solve a question about the volume of a sphere. Here we will calculate the volume of a sphere having a radius of 4 inches.
Solution: Given,
Radius = 4 inches
We know that volume of sphere is = 4/3 π r.r.r
If we calculate, the volume of the sphere comes to 268.08 cubic inches.
