The Base area of a cylinder is the area of the circular base of that cylinder. A right circular cylinder Is a Three-dimensional shape that is made up of a circular base with a curved continuous body. Therefore, the base area of a cylinder is the amount of space occupied by the cylinder when kept on its circular base. There are different types of cylinders: slanted cylinder, cylinder with an elliptical base, cylinder with a non-parallel base; there can be a number of variations in the structure of the cylinder. In this article, we will primarily discuss the base area of the cylinder, which is a right circular cylinder.
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Definition of Base Area of Cylinder
To understand the base area of a cylinder, let us first analyse the three-dimensional shape of the cylinder. A right circular cylinder is made up of two circular bases and a rectangle, which makes the curved tubular body of the cylinder.
Thus, the base area of the cylinder will be the area of the circle which can be calculated if we know the radius of the base of the given cylinder. The total surface area of the cylinder is the area of the rectangular body with the area of circular base and top. If the total surface area of the cylinder is given, to find the base area of cylinder we will need the height of the cylinder with which we can find the radius of the cylinder to get the base area of cylinder.
The Formula of Base Area of Cylinder
Let us calculate the base area of the cylinder. Let there be a cylinder whose height is h and base radius is r.
Base area of cylinder = Area of circle (base) = 𝜋r2
The unit of the base area of a cylinder is unit square or (unit)2
How to Find the Base Area of Cylinder
- To find the base area of cylinder, we simply put the value of radius into the formula to get the value of the base area of the cylinder.
- To find the base area of a cylinder if the total surface area of the cylinder is given, find the radius of cylinder then put it in the formula to find the base area of cylinder.
- To find the base area of cylinder if the curved surface area of cylinder is given, divide the curved surface area by 2𝜋h to get the value of the radius, then find the base area of the cylinder using the formula.
- If the volume of the cylinder is given, to find the base area of the cylinder we just have to divide the height of the cylinder from the volume of the cylinder.
- Always keep in mind to convert all the given quantities in the same system of unit before moving forward with the calculations.
Circumference of Base of Cylinder
The circumference of the base of the cylinder is the perimeter of the circular base of the cylinder. For a cylinder, the circumference of the base or perimeter of the base is the length of the rectangular curved body of the cylinder.
The Formula for Circumference of Base of Cylinder
The formula for the circumference of the base of the cylinder is the same as the circumference of the circle or perimeter of the circle.
Circumference of the base of the circle = 2𝜋r
If the curved surface area of the cylinder is given, the circumference of the base of the circle can be found by dividing the curved surface area by the height of the cylinder.
Articles Related to Base Area of Cylinder
- Cylinder and its properties
- Area of Shapes
- The volume of a Cylinder
- The surface area of the cylinder
- Curved Surface Area of Cylinder
Solved Examples on Base Area of Cylinder
Example 1:
Calculate the base area of the cylinder whose diameter is 1m.
Solution:
Diameter of cylinder = 1 m = 100 cm
Radius of cylinder = 100/2 = 50cm
Base area of cylinder = 𝜋r2 = 3.14 × 502 = 7850 cm2= 78.50 m2
Example 2:
The volume of a cylinder whose height is twice the radius is 17,248 cm2. Find the base area of the cylinder.
Solution:
Let x be the radius of the cylinder then 2x will be its height.
Volume of cylinder = 𝜋r2h = 17248 cm2
∴ 22/7 × x2× 2x = 17248
x3 = (17248 × 7)/44
x = (2744)1/3 = 14 cm
Base area of cylinder = 𝜋r2 = 22/7× 14 × 14 = 616 cm2
Example 3:
A cylindrical tumbler has a base area of 154 square inches. Find the radius of the
tumbler.
Solution:
Base area of cylinder = 𝜋r2= 154
∴ 22/7 × r2 = 154
⇒ r2 = 49
⇒ r = 7 inches
Radius of the tumbler is 7 inches.
Frequently Asked Questions (FAQs on Base Area of Cylinder)
What is meant by the base area of the cylinder?
The base area of a cylinder means an area of the circular base of the cylinder, which can be determined by knowing the radius of the cylinder.
Which formula is used to find the base area of a cylinder?
The base area of a cylinder is given by 𝜋r2 where r is the radius of the base of the cylinder.
How can we find the volume of the cylinder if the base area of the cylinder is given?
Generally, the volume of any three-dimensional shape is the product of the base area and height of that shape. Thus, if the base area of the cylinder is given we can find the volume by multiplying the height of the cylinder to the base area of the cylinder.
How to find the base area of a cylinder if the circumference of the base is given?
The base area of a cylinder can be found by dividing 2𝜋 from the given circumference of the base to find the radius of the cylinder, then substituting the value of radius in the formula of the base area of the cylinder, that is, 𝜋r2 .
What happens to the base area of a cylinder, if the radius is doubled or halved?
If the radius is doubled then the base area becomes four times the original base area of the cylinder. If the radius is halved the base area becomes one-fourth of the original base area of the cylinder.
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