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Calculating volume is a mathematical process that allows us to determine the amount of space occupied by a three-dimensional object. Whether it is finding the volume of a regular shape like a cube or cylinder, or a more irregular shape like a cone or sphere, volume calculations are crucial in various fields such as engineering, construction, and even everyday life. Understanding how to calculate volume not only provides us with a deeper understanding of shapes and their dimensions but also helps us solve real-world problems involving quantities of items or substances. In this article, we will explore different methods and formulas to calculate volume accurately and efficiently, empowering us with a valuable skill that can be applied to a wide range of situations.
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The volume of a shape is a value that indicates how much of a three-dimensional space the shape occupies. [1] XResearch Source You can also imagine the volume of a shape as the amount of water (or air, or sand, etc.) that the shape can hold when filled with the above objects. Common units of volume include cubic centimeters (cm 3 ), cubic meters (m 3 ), cubic inches (in 3 ), and cubic feet (ft 3 ). [2] XResearch Resources This article will show you how to calculate the volume of 6 three-dimensional cubes commonly encountered in math tests, including cube, rectangle, cylinder, pyramid, conical and spherical. You may find that the formulas for volume have the same parts that you can use to remember them. Follow the steps below to see if you can spot the similarities!
Steps
Calculating the Volume of a Cube
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- A six-sided die is an example of a cube that you might find at home. Sugar tablets or children’s literacy blocks are also often cube-shaped.
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- To find s 3 , you just need to multiply s by itself 3 times, ie: s 3 = s * s * s
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- If you are not 100% sure that the cube you are measuring is a cube, measure all the sides and see if the values are equal. If they are not equal, you need to apply the method of calculating the volume of the rectangular box that will be described in the next section.
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Calculating the Volume of a Rectangular
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- A cube is a special form of a rectangular box with the sides of the rectangular box being equal.
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- For example, the length of the rectangular box is 4 inches, so l= 4 in.
- However, you do not need to worry too much about determining which is the length, which is the width, and which is the height. When you measure the sides of the rectangular box and you get 3 different values, the final calculation result will be the same no matter how you arrange the elements.
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- Example: The width of the rectangular box is 3 inches, so w = 3 in.
- If you are measuring the side of a rectangular box with a ruler or tape measure, be sure to use the same unit of measure for all measurements. Don’t measure one side in inches and the other in centimeters; All measurements need to have the same unit of measure!
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- Example: The height of the rectangular box is 6 inches, so h = 6 in.
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- From the above examples, we have: l = 4 in, w = 3 in, h = 6 in. So, V = 4 * 3 * 6, or 72.
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- If the values of the length, width, and height of the rectangular box are: l = 2 cm, w = 4 cm, and h = 8 cm, then the volume will be: 2 cm * 4 cm * 8 cm, or 64 cm 3 .
Calculating the Volume of a Circular Cylinder
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- An AA or AAA battery is usually round in shape.
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- In some geometry questions, the answer may be given as a ratio of pi, but in most cases we can round off and take the value of pi to be 3.14. Ask your teacher which format you should use.
- The formula for calculating the volume of a circular cylinder is very similar to the formula for calculating the volume of a rectangular box: multiply the height (h) by the area of the base. For a rectangular box, the area of the base is l * w, for a circular cylinder, the area of the base of a circle of radius r is πr 2 .
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- Another way to calculate the radius is to measure the circumference of the base (the length of the circle’s outline) with a tape measure or a piece of string that you can mark, then measure again with a ruler. Once you get the circumference, you apply the following formula: C(Perimeter) = 2πr. Divide the circumference by 2π (or 6.28) and you will find the value of the radius.
- For example, if the circumference you measured was 8 inches, the radius would be 1.27 in.
- If you want to find the really exact value of the circumference, you can apply and compare the results obtained from the two methods above, if the results are significantly different, check again. The circumferential method will usually give more accurate results.
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- If the radius of the circle is 4 inches (10.16 cm), the area of the base will be A = π4 2 .
- 4 2 = 4 * 4, or 16. 16 * (3.14) = 50.24 in 2
- If the diameter of the base is known, remember the formula: d = 2r. You just need to divide the value of the diameter by 2 to get the value of the radius.
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- V = 4 2 10
- 4 2 = 50.24
- 50.24 * 10 = 502.4
- V = 502.4
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Calculate the volume of the pyramid
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- We often imagine a pyramid with a square base and its faces intersecting at one point, but the base of a pyramid can have 5, 6, or even 100 sides!
- A pyramid whose base is a circle is called a cone, we will talk about the volume of the cone later.
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- The formula for the volume of a regular pyramid is the same as above, in that the projection of the vertex of the polygon to the base is the center of the base, and for an oblique pyramid, the projection of the vertex to the base is not the center of the base. bottom.
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- The formula for the volume of a pyramid whose base is a triangle is: A = 1/2bh, where b is the area of the base and h is the height.
- We can calculate the area of any polygon by applying the formula A = 1/2pa, where A is the area, p is the perimeter and a is the midpoint, the midpoint is the distance from the center of the polygon. of the polygon to the midpoint of any side. This formula is beyond the scope of this article, but you can also see how to calculate the area of a polygon for a better understanding of how to apply the above formula.
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- If we have another pyramid with a base of a pentagon with area 26, height 8, volume of this pyramid will be 1/3 * 26 * 8 = 69.33.
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Calculating the Volume of a Cone
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- If the projection of the vertex to the base of the cone coincides with the center of the base, it is called a “regular cone”. Otherwise we call it “oblique cone”. However, the formula for the volume of both cones is the same.
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- In the above formula, πr 2 is the area of the base surface. From this we can see that the formula for calculating the volume of the cone is 1/3bh, which is the same formula for calculating the volume of the pyramid that we considered above.
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- For the example given in the diagram, the radius of the base of the cone is 3 inches. Substituting this value into the formula, we have: A = π3 2 .
- 3 2 = 3 *3, or 9, so A = 9π.
- A = 28.27 in 2
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- So, in this example, the volume of the cone is 141.35 * 1/3 = 47.12.
- We can reduce the recalculation steps and get 1/3π3 2 5 = 47.12
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Calculating the Volume of a Sphere
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- For example, if you measure a ball and get the circumference of the ball to be 18 inches, divide that number by 6.28 and you get the value of the radius to be 2.87 in.
- Measuring a sphere can take some ingenuity, so to get the most accurate results possible, you should measure 3 times and then average the value (add the value obtained after 3 measurements). again and then divide by 3).
- For example, if the circumference you get after 3 measurements is 18 inches, 17.75 inches, and 18.2 inches, add these values together (18 + 17.5 + 18.2 = 53.95) ) and divide the total found by 3 (53.95/3 = 17.98). Use this value to calculate the volume.
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- In the example under consideration, 36 * 3.14 = 113.04.
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wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 32 people, some of whom are anonymous, have edited and improved the article over time.
There are 11 references cited in this article that you can view at the bottom of the page.
This article has been viewed 252,632 times.
The volume of a shape is a value that indicates how much of a three-dimensional space the shape occupies. [1] XResearch Source You can also imagine the volume of a shape as the amount of water (or air, or sand, etc.) that the shape can hold when filled with the above objects. Common units of volume include cubic centimeters (cm 3 ), cubic meters (m 3 ), cubic inches (in 3 ), and cubic feet (ft 3 ). [2] XResearch Resources This article will show you how to calculate the volume of 6 three-dimensional cubes commonly encountered in math tests, including cube, rectangle, cylinder, pyramid, conical and spherical. You may find that the formulas for volume have the same parts that you can use to remember them. Follow the steps below to see if you can spot the similarities!
In conclusion, calculating volume is a fundamental skill that is essential in various fields such as mathematics, science, engineering, and architecture. It allows us to determine the amount of space occupied by an object in three-dimensional space. The process involves understanding the shape of the object, measuring its dimensions, and applying the appropriate formula or method to find the volume. By calculating volume, we can solve real-life problems, design structures, analyze data, and make informed decisions. It is a valuable skill that is not only practical but also helps develop critical thinking and problem-solving abilities. While the formulas for finding volume may differ depending on the shape of the object, the underlying concept of measuring the amount of space remains the same. With practice and knowledge of the necessary formulas, anyone can learn how to accurately calculate volume and apply it to solve various mathematical and practical problems.
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