Buzz
As you know, a circular cylinder is a shape with two parallel circular bases, which are equal. Some examples of cylindrical objects include milk cans, cups, vases, barrels, buckets, etc. Calculating the volume of a cylinder is quite simple and has many practical applications. So let's take a look at how to calculate the volume of a cylinder.
Calculating the volume of a circular cylinder and example exercises.
I. Formula for Calculating the Volume of a Cylinder
- To calculate the volume of a circular cylinder, we use the following formula:V = π. r2. h
Where:
- V represents volume
- r is the radius of the circular base of the cylinder
- h is the height of the cylinder
- π is a constant ( π = 3.14)
- Volume unit: cubic meter (m3)
- In words: To find the volume of a cylinder, multiply the height by the square of the radius of the circular base of the cylinder and pi.
Illustrative Example: Calculate the volume of a cylinder given that the radius of both bases is 7.1 cm and the height is 5 cm.
Problem-solving guide: To solve the exercise, simply apply the formula for the volume of a cylinder, substitute the values, and calculate. We have, the volume of the cylinder is: 3.14 x (7.1)2 x 5 = 791.437 (cm3)
Students apply the formula for the volume of a cylinder above to solve exercises related to finding the volume of a circular cylinder, finding the volume of a cylinder circumscribed about a cube with side length a, finding the volume of a cylinder with a base radius equal to a inscribed in a sphere with radius 2a,...
II. Finding Parameters in Cylinder Volume Problems
1. Finding the Base Radius
- You can calculate either base because both bases are equal.
- If you don't know the measurement of the base radius, use a ruler to measure the widest distance across the circle, then divide the result by 2 because r = 1/2.d (d represents the diameter).
Example: You measure a distance of 5 cm, to find the radius r, you divide 5 by 2, resulting in 2.5 (cm)
* Note: The diameter is the longest chord in a circle, therefore, when measuring the diameter, choose a point on the edge of the circle as the starting point, then measure the maximum length without shifting the starting point to find the length of the diameter.
2. Finding the Area of the Circular Base
- To find the area of the circular base, we use the formula for the area of a circle: A = π.r2 where A represents the area of the circular base, r is the radius of the circle (base of the cylinder).
Example: Find the area of the circular base given r = 6.5 cm.
=> The area of the circular base is: 3.14 x (6.5)2 = 132.665 (cm2)
3. Finding the Height of the Cylinder
- The height of the cylinder is defined as the distance between the two bases on the lateral surface.
- If you don't know the height of the cylinder, you can use a ruler to accurately measure the length of the vertical line and substitute it into the formula to calculate the volume of the cylinder.
The formula for finding the volume of a cylinder and applying it to solve problems involving finding parameters when knowing the volume of a prism is quite easy to understand and remember. Therefore, students can easily memorize it to apply it to solve simple problems. In addition, students should also refer to additional exercises on finding the volume of a cylinder circumscribed about a cube with side length a and articles sharing formulas for finding the area of a cylinder shared on Mytour to fully understand all types of cylinder problems. If there are any good problem-solving methods, students can share them with us to make problem-solving faster and simpler. We hope students always have a passion for Mathematics in general and Geometry in particular.
III. Example Solving Exercises on the Area and Volume of a Cylinder in Textbooks
1. Solve problem 6 Math 9 exercise 2 in textbook page 111
The height of a cylinder is equal to the radius of the circular base. The lateral surface area of the cylinder is 314 cm2. Calculate the radius of the circular base and the volume of the cylinder (round the result to the second decimal place).
Problem-solving Instructions
Calculate:
a) The lateral surface area of a cylinder with a circumference of the circular base is 13cm and a height of 3cm.
b) The volume of a cylinder with a radius of the circular base is 5mm and a height of 8mm.
Problem-solving Instructions
3. Problem 11 page 112 Textbook Math 9 Exercise 2
Review and understand how to calculate the area of a circle in plane geometry. This fundamental knowledge will help you tackle circle-related problems with ease.
