How To Find The Volume
How you measure the volume of something is going to depend on what you are measuring. The volume of sound is measured by looking at the sound wave, while the volume of objects is measured using volume formulas. Now that you have learned plenty of different ways to measure volume, check out examples of gas to solids.
Calculating The Volume Of A Cylinder
Volume Of Cylinders Explanation & Examples
The volume of a cylinder is the measure of the amount of space occupied by a cylinder or the measure of the capacity of a cylinder.
This article will show you how to find the volume of a cylinder by using cylinder volume formula.
In geometry, a cylinder is a 3-dimensional shape with two equal, and parallel circles joined by a curved surface.
The distance between the circular faces of a cylinder is known as the height of a cylinder. The top and bottom of a cylinder are two congruent circles whose radius or diameter are denoted as r and d, respectively.
Finding The Ratio Between Mass And Volume
- Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
- B.A., Physics and Mathematics, Hastings College
density = mass/volume
The mass is usually the easy part while finding volume can be tricky. Simple shaped objects are usually given in homework problems such as using a cube, brick or sphere. For a simple shape, use a formula to find volume. For irregular shapes, the easiest solution is to measure volume displaced by placing the object in a liquid.
This example problem shows the steps needed to calculate the density of an object and a liquid when given the mass and volume.
How Do You Find The Height Of A Cylinder
If you have the volume and radius of the cylinder:
If you have the surface area and radius :
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Calculate Volumes Of Gases
- Avogadros Law states that at the same conditions of temperature and pressure, equal amounts of gases occupy the same volume of space
- At room temperature and pressure, the volume occupied by one mole of any gas was found to be 24 dm3 or 24,000 cm3
- This is known as the molar gas volume at RTP
- RTP stands for room temperature and pressure and the conditions are 20 ºC and 1 atmosphere
- From the molar gas volume the following formula triangle can be derived:
Formula triangle showing the relationship between moles of gas, volume in dm3 and the molar volume
Formula triangle showing the relationship between moles of gas, volume in cm3 and the molar volume
To find the volume
Volume = Moles x Molar Volume
Examples of Converting Moles into Volumes Table
To find the moles
Show Students Five Rods That Have The Same Mass But Different Volumes
Show students the five rods and explain that they all have the same mass. Then hold up the longest, middle-sized, and shortest rods and remind students that they have the same mass.
Ask students to make a prediction:
Students may reason that since the mass of each rod is the same, the volume of each rod must have something to do with its density. Some may go so far as to say that the rod with the smallest volume must have the highest density, because the same mass is packed into the smallest volume. Or that the rod with the largest volume must have the lowest density, because the same mass is spread out over the largest volume.
Tell students that like the cubes in the previous activity, they will need to know the volume and mass of each of the samples. They will also calculate the density of each sample and use this value to figure out which material each rod is made of.
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Key Takeaways: How To Calculate Density
- Density is how much matter is contained within a volume. A dense object weighs more than a less dense object that is the same size. An object less dense than water will float on it one with greater density will sink.
- The density equation is density equals mass per unit volume or D = M / V.
- The key to solving for density is to report the proper mass and volume units. If you are asked to give density in different units from the mass and volume, you will need to convert them.
Question 1: What is the density of a cube of sugar weighing 11.2 grams measuring 2 cm on a side?
Step 1:Find the mass and volume of the sugar cube.
Mass = 11.2 gramsVolume = cube with 2 cm sides.
Volume of a cube = 3Volume = 3
Step 2: Plug your variables into the density formula.
density = mass/volumedensity = 1.4 grams/cm3
Answer 1: The sugar cube has a density of 1.4 grams/cm3.
Question 2: A solution of water and salt contains 25 grams of salt in 250 mL of water. What is the density of the salt water?
Step 1: Find the mass and volume of the salt water.
This time, there are two masses. The mass of the salt and the mass of the water are both needed to find the mass of the salt water. The mass of the salt is given, but the only the volume of water is given. We’ve also been given the density of water, so we can calculate the mass of the water.
Answer 2: The salt water has a density of 1.1 grams/mL.
How Do I Determine Density
Another tricky thing about density is that you can’t add densities. If I have a rock that is made up of two minerals, one with a density of 2.8 g/cm3, and one with a density of 3.5 g/cm3, the rock will have a density between 3.5 and 2.8 g/cm3, not a density of 6.3 g/cm3. This is because both the mass and the volume of the two minerals will be added, and so when they are divided to get the density the result will be between the two.
Typical densities for gasses are on the order of thousandths of grams per cubic centimeter. Liquids often have densities of about 1.0 g/cm3, and indeed, fresh water has a density of 1.0 g/cm3. Rocks often have a density around 3 g/cm3, and metals often have densities above 6 or 7 g/cm3.
How To Calculate Mass
This article was co-authored by Sean Alexander, MS. Sean Alexander is an Academic Tutor specializing in teaching mathematics and physics. Sean is the Owner of Alexander Tutoring, an academic tutoring business that provides personalized studying sessions focused on mathematics and physics. With over 15 years of experience, Sean has worked as a physics and math instructor and tutor for Stanford University, San Francisco State University, and Stanbridge Academy. He holds a BS in Physics from the University of California, Santa Barbara and an MS in Theoretical Physics from San Francisco State University.There are 8 references cited in this article, which can be found at the bottom of the page. This article has been viewed 993,410 times.
Mass is one of the fundamental properties of an object in Physics, and is a measurement of how much matter there is in something. Matter is any substance that you can touch anything that takes up physical space and has volume. Often, mass is related to size, but this isnt a perfect relationship, as objects like a large hot-air balloon often have less mass than a small boulder. To calculate mass, youll first need the density and volume of the object. Read on for details of the formula and to learn about different types of mass across scientific disciplines.
Discuss The Density Of Calcium Compared To The Density Of Sulfur
Have students refer to the illustration of calcium and sulfur on their activity sheets. Explain that a calcium atom is both bigger and heavier than a sulfur atom. But a piece of solid sulfur is more dense than a solid piece of calcium. The density of sulfur is about 2 g/cm3 and the density of calcium is about 1.5 g/cm3.
- Based on what you know about the size, mass, and arrangement of atoms, explain why a sample of sulfur is more dense than a sample of calcium.
- Even though a sulfur atom has less mass than a calcium atom, many more sulfur atoms can pack together in a certain amount of space. This gives sulfur more mass per volume than calcium, making it more dense.
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Is Pressure * Volume Energy
Pressure in a fluid may be considered to be a measure of energy per unit volume or energy density. The most obvious application is to the hydrostatic pressure of a fluid, where pressure can be used as energy density alongside kinetic energy density and potential energy density in the Bernoulli equation.
How Do I Measure Volume
Measuring the volume depends on your object’s state of matter. For liquids, you can use a graduated cylinder or burette for the chemistry lab measurements, or a measuring cup & spoon for everyday life purposes. For gases, to roughly measure the volume, you can inflate a balloon and use it to displace the water in a graduate cylinder. A similar method works for solids put the object into a graduated container and measure the change in reading.
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Volume Of Prisms And Cylinders
This basic formula can be extended to cover the volume of cylinders and prisms too. Instead of a rectangular end, you simply have another shape: a circle for cylinders, a triangle, hexagon or, indeed, any other polygon for a prism.
Effectively, for cylinders and prisms, the volume is the area of one side multiplied by the depth or height of the shape.
The basic formula for volume of prisms and cylinders is therefore:
Area of the end shape × the height/depth of the prism/cylinder.
Watch out for inconsistent units!
A straight length of circular pipe has an internal diameter of 2cm and a length of 1.7m. Calculate the volume of water in the pipe.
In this example you need to calculate the volume of a very long, thin cylinder, that forms the inside of the pipe. The area of one end can be calculated using the formula for the area of a circle r2. The diameter is 2cm, so the radius is 1cm. The area is therefore × 12, which is 3.14cm2.
The length of the pipe is 1.7m, so you need to multiply the end area by the length in order to find the volume.
Watch out for inconsistent units! The area is in centimetres, but the length is in metres. First convert the length into cm 1.7 × 1000 = 1700cm.
The volume is therefore 3.14 × 1700 = 5338 cm3. This is equivalent to 5.338 litres, or 0.0053 m3.
How Do You Draw A Cylinder
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What Is Meant By The Volume Of A Cylinder
In mathematics, the volume of a cylinder is defined as the region occupied by the three-dimensional shape cylinder. The volume is represented by cubic units. The 3D shape cylinder can be obtained by the rotation of the two-dimensional shape rectangle. The formula to calculate the volume of a cylinder is given by
The volume of the cylinder, V = r2h cubic units
How Do You Find The Volume Of A Right Trapezoidal Cylinder
A right trapezoidal cylinder, also known as a rectangular prism, can be solved as such:
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How To Calculate Volume Volume Formulas
There is no simple answer to this question, as it depends on the shape of the object in question. Here are the formulas for some of the most common shapes:
Cube = s³, where s is the length of the side.
Sphere = r³, where r is the radius.
Cylinder = r²h, where r is the radius and h is the height.
Cone = r²h, where r is the radius and h is the height.
Rectangular solid = lwh, where l is the length, w is the width and h is the height .
Pyramid = Ah where A is a base area and h is the height. For a pyramid with a regular base, other equation may be used as well: Pyramid = * h * side_length² * cot, where n is a number of sides of the base for a regular polygon.
Prism = Ah, where A is a base area and h is the height. For a right triangular prism, the equation can be easily derived, as well as for a right rectangular prism, which is apparently the same shape as a box.
How To Find The Volume Of A Rectangle Vs Volume Of A Box
You can’t calculate a volume of a rectangle, a volume of a circle or a volume of a square because they are 2-dimensional geometric figures. As such, a rectangle does not have a volume . What you’re probably looking for is the volume of a rectangular cuboid , which is a 3-dimensional object.
To find the volume of a box, simply multiply length, width, and height and you’re good to go! For example, if a box is 5×7×2 cm, then the volume of a box is 70 cubic centimeters.For dimensions that are relatively small whole numbers, calculating volume by hand is easy. For larger or decimal valued numbers, the use of the volume calculator is very efficient.
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Measuring Mass With A Balance