ClassX Video Lessons Youtube Channel TutoringHour Volume of a Cylinder | Learn through Cool Illustrations
Welcome to an exciting journey of learning about cylinders! Cylinders are all around us, from soup cans to candles, perfume bottles, bass drums, and even large water tanks. Today, we’ll dive into understanding how to calculate the volume of these fascinating shapes.
Volume is a measure of how much space an object takes up in three dimensions. For a cylinder, we find the volume by multiplying the area of its base by its height. But how do we find the area of the base?
The base of a cylinder is a circle. To find the area of a circle, we use the formula: π times the radius squared (πr²). Here, “r” stands for the radius of the circle. Once we have the area of the base, we multiply it by the height of the cylinder to get the volume. So, the formula for the volume of a cylinder is: π times r squared times h (πr²h).
Let’s put this formula to use with a cylindrical candle. Suppose the candle is 16 cm tall, and the radius of its base is 3 cm. Using our formula, we calculate:
Volume = π times (3 cm)² times (16 cm) = π times 9 cm² times 16 cm = π times 144 cm³.
This gives us a volume of 144π cubic centimeters. If we want a numerical value, we can use π ≈ 3.14. Doing the math, we find the volume is approximately 452.16 cubic centimeters.
Now, imagine Rhea is setting up a cylindrical aquarium. The aquarium is 12 inches tall with a diameter of 9 inches. First, we need to find the radius, which is half of the diameter. So, the radius is 4.5 inches.
Using the volume formula, we have:
Volume = π times (4.5 inches)² times (12 inches).
Squaring the radius gives us 20.25 inches². Multiplying this by the height, we get 243π cubic inches. Using π ≈ 3.14, the approximate volume of the aquarium is 763.02 cubic inches.
Now it’s your turn to practice! You can find more examples and exercises at tutoringhour.com. Have fun exploring the world of cylinders!
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Using construction paper, scissors, and tape, create a model of a cylinder. Measure the radius and height of your cylinder, then calculate its volume using the formula πr²h. Share your model and calculations with the class.
Look around your home or classroom for cylindrical objects. Measure their dimensions and calculate their volumes. Create a list of at least three objects, including their calculated volumes, and present your findings to the class.
Work in pairs to solve a set of volume problems involving cylinders with different dimensions. Each pair will receive a worksheet with problems to solve. Compare your answers with another pair and discuss any differences in your calculations.
Use an online tool or drawing software to design a cylindrical aquarium. Decide on the dimensions and calculate the volume. Present your design to the class, explaining why you chose those dimensions and how much water it can hold.
Create a story problem involving the volume of a cylinder. Include real-life scenarios, such as filling a tank or baking a cake. Exchange problems with a classmate and solve each other’s challenges.
Sure! Here’s a sanitized version of the YouTube transcript:
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Hello and welcome to Tutoring Hour!
In this video, we will explore the concept of cylinders, including examples like a soup can, a candle, a bottle of perfume, a bass drum, and a large water tank.
Volume is the measure of how much three-dimensional space an object occupies. The volume of a cylinder is calculated by multiplying the area of its base by its height.
Let’s take a look at a cylinder with a circular base. The area of the circular base is calculated using the formula π times r squared, where r is the radius of the base. Therefore, the volume is equal to the area of the base times the height of the cylinder, which can be expressed as π times r squared times h.
Now, let’s apply this formula to find the volume of a cylindrical candle. The height of the candle is 16 cm, and the radius of its base is 3 cm.
Using the formula, we have:
Volume = π times (3 cm)² times (16 cm)
= π times 9 cm² times 16 cm
= π times 144 cm³.
This can also be expressed as 144π cubic centimeters. We can either stop here or substitute the value of π, which is approximately 3.14.
Calculating this gives us the volume of the candle as approximately 452.16 cubic centimeters.
Now, let’s consider another example. Rhea is setting up a cylindrical aquarium at her home. The aquarium measures 12 inches in height and has a diameter of 9 inches.
First, we need to find the radius, which is half the diameter. Dividing the diameter (9 inches) by 2 gives us a radius of 4.5 inches.
Now, we can use the formula for the volume of the cylinder:
Volume = π times (4.5 inches)² times (12 inches).
Squaring the radius gives us 20.25 inches². Multiplying this by the height results in 243π cubic inches.
Substituting the value of π (approximately 3.14), we find the approximate volume of the aquarium to be 763.02 cubic inches.
Now it’s your turn! If you want to practice more, visit tutoringhour.com.
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This version maintains the educational content while ensuring clarity and professionalism.
Volume – The amount of space that a three-dimensional object occupies, measured in cubic units. – The volume of a cube can be found by multiplying the length of one side by itself three times.
Cylinder – A three-dimensional shape with two parallel circular bases connected by a curved surface. – To find the volume of a cylinder, you need to know the radius of its base and its height.
Area – The measure of the surface of a shape, expressed in square units. – The area of a rectangle is calculated by multiplying its length by its width.
Base – The bottom surface of a three-dimensional object, or one of the sides of a two-dimensional shape, used as a reference for measurement. – In a triangle, the base can be any one of its sides, and the height is measured perpendicular to it.
Radius – The distance from the center of a circle to any point on its circumference. – The radius of a circle is half of its diameter.
Height – The perpendicular distance from the base to the top of a shape or object. – To find the volume of a cone, you need to know its base radius and height.
Formula – A mathematical rule expressed in symbols, used to calculate values. – The formula for the area of a circle is π times the square of the radius.
Circle – A round plane figure whose boundary consists of points equidistant from a fixed center point. – The circumference of a circle can be calculated using the formula 2πr, where r is the radius.
Inches – A unit of linear measure equal to 1/12 of a foot, commonly used in the United States. – The length of the rectangle is 8 inches, and its width is 5 inches.
Centimeters – A metric unit of linear measure equal to one hundredth of a meter. – The diameter of the circle is 10 centimeters, so its radius is 5 centimeters.
