Introduction
The total area that the flat surface at the base of a cylinder occupies is the definition of the base area. Calculating the areas of the two bases and the curved surface allows us to determine the overall surface area of a cylinder.
Since the base area of the cylinder is a circle, the base area is the same as the area of a circle. Just like other measures of area, the base area is expressed as the number of square units such as square feet, square inches, square centimeters and other related units.
Define Base Area of a Cylinder
First, let’s examine the three – dimensional shape of a cylinder in order to comprehend the base area. Two circular bases, a rectangle, and the curving tubular body of the cylinder create a right circular cylinder.
As a result, if we know the radius of the base of a given cylinder, we may compute the base area of the cylinder as the area of the circle. The overall surface area of the cylinder consists of its rectangular body plus its rounded base and top. If the whole surface area of the cylinder is known, finding the base area of the cylinder requires knowing its height in order to determine its radius and, ultimately, its base area.
Formulation
By multiplying the square of the radius of a cylinder by π, we can determine the base area. As a result, ‘πr\(^2\)’ is the formula for the base area, and as mentioned the formula is the same as the one used to calculate the area of any circle, with a given radius, r.
Cylinder Base Area = (π × r\(^2\)) square units.
How do you determine the Base Area of the Cylinders?
The square of the radius multiplied by determines its base area. The steps listed below can be used to determine its base area.
Step 1: Calculate the base radius of the cylinder.
Step 2: Find the square of the radius.
Step 3: Find the product of the square of radius and the value of π.
Step 4: The solution is expressed in square units.
Solved Examples
Example 1: Find the base surface area of a cylinder consisting of a base radius of 10 inches.
Solution:
As stated, base radius of the cone = 10 inches
Base area of the given cylinder = π × r\(^2\) [Use formula]
= \(\frac{22}{7}\) × (10)\(^2\) [Substitute the value of r]
= \(\frac{22}{7}\) × 100 [Apply PEMDAS rule]
= 3.1428 × 100 [Divide 22 by 7]
= 314.28 in\(^2\) [Multiply]
So, the base area of the cylinder is 314.28 square inches.
Example 2: Find the base area of the cylinder whose base radius is 134 centimeters.
Solution:
Data: Base radius of the cone = 134 centimeters
Base area of the given cylinder = π × r\(^2\) [Use formula]
= \(\frac{22}{7}\) × (134)\(^2\) [Substitute the value of r]
= \(\frac{22}{7}\) × 17956 [Apply PEMDAS rule]
= 3.1428 × 17956 [Divide 22 by 7]
= 56432.11 cm\(^2\) [Multiply]
So, the base area of a cylinder is 56432.11 square centimeters.
Example 3: Find the base area of a cylindrical oil tanker having a base radius of 2 meters.
Solution:
Data: Base radius of the cylindrical oil tanker = 2 meters
Base area of the given cylinder = π × r\(^2\) [Use formula]
= \(\frac{22}{7}\) × (2)\(^2\) [Substitute the value of r]
= \(\frac{22}{7}\) × 4 [Apply PEMDAS rule]
= 3.1428 × 4 [Divide 22 by 7]
= 12.57 m\(^2\) [Multiply]
So, the base area of a cylindrical oil tanker is 12.57 square meters.
The square of the radius multiplied by 3.14 or 22/7, the value of ‘pi’ determines its base area.
The area occupied within the perimeter of the circular base is referred to as the base area of the cylinder. The base area of the cylinder is expressed in square millimeters, square inches, and square feet and related units used to express the area of a geometric shape.
The base area of a cylinder can be calculated using the formula ‘pi multiplied by the square of the radius r’. Due to its circular base, the value of the base area is equal to the area of the circle.