## How To Find The Volume Of A Cylinder

Cylinder — stereometric geometric figure formed by the rotation of a rectangle about one of its sides, and having the following grounds. A physical example of the cylinder can be a piece of wire, tube. To determine the volume of the cylindrical body, you need to first determine what type of cylinder it has.

### Instruction how to find the volume of a cylinder

Step 1:

If the body has a conventional cylinder, its volume is the product of the height at the base area. The basis for such a cylinder is a circle whose area is calculated as the product of the number of «pi» to the square of the radius ratio of the product or the number of «pi» to the square of the diameter of the four. S = π * (R) squared or S = π * (D) squared / 4. Then, the full volume of the cylinder is calculated by the formula: V = h * π * (R) squared or V = h * π * (D) squared / 4. Example 1. It is necessary to find the volume of the cylinder when its base is equal to the radius of 15cm, and its height 10 sm.Reshenie 1: V = h * π * (R) = 10 square cm * 3.14 * 15 * 15 = 7065 cu cm . Solution 2: Knowing that the diameter is twice the radius to find the diameter: D = 2 * 15cm = 30cm. Then, V = h * π * (D) squared / 10cm = 4 * 3.14 * 30 * 30/4 = 7065 cu cm.

Step 2:

Another type of cylinder is called a hollow cylinder, hollow cylinder or tube. Its volume is difficult, given the more complex geometry of the figure (see. Figure). If we introduce the notation: R — radius of the great circle of foundation, r — the radius of the small circle of the base, h — the height of the cylinder, then the volume of the pipe is calculated as follows: V = π * ((R) in the square — (r) squared) * h . Example 2. Suppose it is necessary to find the volume of a hollow cylinder height of 1 m if the outer circle has a radius of 0.5 m and internal — 0.1 m Solution:. V = π * ((R) in the square — (r) squared) * h = 3,14 * 1m (0.5m * 0.5m — 0.1m * 0.1m) = 0.75 cubic meters.

Step 3:

When viewed in the hollow cylinder the outer and inner diameters, introducing the notation of the form: D- great circle diameter, d — diameter of the small circle of the pipe volume formula takes the following form: V = πh / 4 (D squared — d squared) Example 3 . The diameter of the great circle of the cylinder base is 25cm, small — 20 cm Find the volume of a pipe, if its height — 15 cm Solution:.. V = πh / 4 (d squared — d squared) = 3.14 * 15 cm / 4 (625sm-400cm) = 2649 cubic centimeters.

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## How to Calculate the Volume of a Cylinder in Gallons

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The Imperial measurement system can be downright cumbersome, and nothing illustrates this more than its unit of volume, the gallon. No matter what units you use to measure dimensions, you always have an extra step after calculating volume if you want the answer in gallons. The volume of a cylinder depends on two parameters: the radius of its circular cross-section and its length. Measure these in inches or feet, and you’ll get the volume in cubic inches or cubic feet. Measure in metric units and you’ll get the volume in cubic meters, liters or milliliters. In all cases, you have to multiply by a conversion factor to get the volume in gallons. And to make things even more confusing, a gallon in the United States – one of the few countries that still uses gallons – is smaller than a standard Imperial gallon.

##### TL;DR (Too Long; Didn’t Read)

The volume (V) of a cylinder with cross-sectional diameter d and length or height h is given by V = πd^{2}h/4. Convert to gallons using the appropriate conversion factor.

### Useful Conversion Factors

If you want to calculate volume in gallons, you’ll need a few conversion factors. It’s handy to have them all in one place, so here is a table of common conversion factors for U.S. gallons:

**1 cubic inch**= 0.004329 U.S. gallons**1 cubic foot**= 7.4805 U.S. gallons**1 cubic meter**= 264.1720 U.S. gallons**I liter**= 0.264 U.S. gallons**1 milliliter**= 0.000264 U.S. gallons

### How to Calculate the Volume of a Cylinder

The volume of the cylinder is the product of its length or height (h) and the area of its cross-section, which you determine by measuring radius (r). The mathematical formula is:

In practice, it’s usually easier to measure the diameter of the circular cross-section (d) than it is to measure radius. Since radius is half the diameter (r = d/2) the equation becomes A = π (d/2)^{2}h = πd^{2}/2^{2} •h = πd^{2}/4 • h, which simplifies to:

### Sample Calculations

**1. You measure the diameter of a cylindrical water storage tank to be 10 feet and its height to be 13 feet. What is its capacity?**

Its capacity (volume) is π (10^{2} • 13) ÷ 4 = 1,021.02 cubic feet. Convert to U.S. gallons by multiplying by 7.4805. The answer is **7,637.23 gallons.**

**2. A 6-inch water pipe is 5 feet long. How much water can it hold?**

A 6-inch pipe has a circular cross-section with an inside diameter of 6 inches. This makes the radius 3 inches. The length was measured in feet, so to get both measurements in the same units, convert the length to inches: 5 feet = 60 inches. The volume in cubic inches is thus π • 3^{2} • 60 = 1,696.46 cubic inches. Using the conversion factor 1 cubic inch = 0.004329 U.S. gallons, you get the volume as **7.34 U.S. gallons.**

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## How to Figure the Weight of Gas in a Cylinder

Theresa Knott, Wikipedia Commons

When we look at a glass with no water in it or a paint can after all the paint is used, we usually think of it as empty. However, these cylinders aren’t really empty. They are full of gas: the air that surrounds us. Air, as well as gases such as hydrogen and helium, has mass. If you could put a gas on a scale, you’d find it has a specific weight that depends on the density of the particular kind of gas. However, you can figure the weight of gas in a cylinder if you calculate the volume of the cylinder and know the density of the gas it contains.

Find the radius of the cylinder. Wrap a tape measure around the cylinder to measure its circumference. Divide this value by 2 pi (about 6.283) to find the radius of the cylinder. For example, if the cylinder is 26 cm in circumference, the radius is 26 cm/(2 pi), or about 4.12 cm.

Measure the height of the cylinder. To calculate the volume, use the formula V = H x pi x R^2 (volume equals height times pi times the square of the radius). Suppose you have a cylinder 10 cm high and the radius is 5 cm. You calculate V = 10 cm x 3.14 x (5 cm)^2, or about 785 cubic centimeters.

Find the density of the gas in a table of gas densities. Air has a density of 0.128 g per cubic centimeter (this is often listed per milliliter). Different gases have other densities. For example, helium has a density of 0.00018 g per cubic centimeter.

Multiply the volume by the density to figure the weight of gas in the cylinder. A cylinder with a volume of 785 cubic centimeters filled with air contains 785 x 0.128 g, or about 100.48 g of air.

##### Tip

The standard densities of gases listed in tables assume that the atmospheric pressure is normal (about 14.7 pounds per square inch) and that the temperature is about 60 degrees F (15.6 degrees C). If the air pressure is lower, the gas in the cylinder will weigh less. The same is true if the temperature is higher than 60 degrees F because gas expands as temperature rises. Conversely, higher pressures and lower temperatures result in more air in the cylinder.

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## How To Determine The Volume Of A Cylinder

The cylinder as the geometric shape can be parabolic, elliptical, hyperbolic. Even a prism, by definition, is one of the particular forms of the cylinder. However, in most cases under the cylinder mean figure in the grounds which are circles, and the angle between the side surface and the bottom is 90 °. Below is the formula for calculating the volume of such a cylinder.

### Instruction how to determine the volume of a cylinder

Step 1:

If known cylinder base area (S) and its height (H), then multiply the two known values to calculate the volume (V) of the cylinder: V = S∗H. For example, if the base area is two square meters, and height — four meters, the volume of the cylinder is 2∗4 = 8 cubic meters.

Step 2:

If known cylinder base circle radius (R) and its height (H), multiply the number of pi (pi;) by the square of the radius of a known length and its height to calculate the volume (V) shape: V = pi;∗R²∗H. For example, if the base radius of length equal to fifty centimeters, and height — four meters, the volume of the cylinder will be 3.14∗0.5²∗4 = 3.14 cubic meter.

Step 3:

If the known diameter of the circle at the bottom of the cylinder (D) and height (H), the figure is equal to the volume of one quarter of the height of the product by the number of pi (pi;) and the square of the diameter of a circle of known length: V = H∗pi;∗D² / 4. For example, if the diameter of the base is equal to the length of two meters, and height — four meters, the volume of the cylinder is 4∗3.14∗2² / 12.57 = 4 cubic meters.

Step 4:

If you know the length of the base of the cylinder circumference (L) and height (H), then find the volume of a cylinder (V), as a product of its height to the quotient of the square of the circumference into four of pi (pi;): V = H∗L² / (4∗pi;). For example, if the circumference of the base is equal to the length of two meters, and height — four meters, the volume of the cylinder is 4∗2² / (4∗3.14) = 1.27 cubic meter.

Step 5:

Practical calculations in the calculation of the volume values can be produced using a calculator, and you can use the search engine Nigma or Google — it is also built easy-to-use computational algorithm. For example, to calculate the volume of a cylinder with the original data used in the previous step, in Google search query box you can enter the following text: «4 * 2 ^ 2 / (4 * pi).»

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## How To Find The Volume Of A Figure

The figure — a term applied to a variety of sets of points which can be represented by a finite number of points, lines or surfaces. Examples of shapes: cube, sphere, cylinder, pyramid, cone. The volume figures — a quantitative characteristic of the space occupied by the figure. He measured in cubic meters and cubic centimeters. You need to know the volume of figures and formulas to be able to use them as a basis is solid geometry.

#### You will need:

Ruler, calculator.

### Instruction how to find the volume of a figure

Step 1:

First, determine which figure is in front of you. This can be a cube, sphere, cylinder, pyramid, cone. Based on this, find the volume of the figure.

Step 2:

If you have determined that the cube in front of you. Cube — a regular polyhedron, each face of which is a square. To find its volume, measure the line side of the cube and bring the resulting number in the cube.

Step 3:

If you determine that the ball in front of you. Ball — is the set of all points in space that are located at a distance of not more given to the center. To find its volume, multiply the number of 4/3 «pi» to the radius of the sphere in the cube or 1/6 «pi» to the diameter cubed.

Step 4:

If you have determined that the cylinder in front of you. The cylinder — a geometric body bounded by a cylindrical surface and two parallel planes that intersect it. To find its volume, to multiply the cylinder pi squared radius and height.

Step 5:

If you determine that the pyramid in front of you. Pyramid — a polyhedron whose base — polygon, and the other side — the triangles having a common vertex. To find its volume, multiply the third base side of the pyramid to its height.

Step 6:

If you determine that before you cone. Cone — a body obtained by combining all of the rays emanating from one point passing through the flat surface. To find its volume, multiply 1/3 «pi» to the cone radius squared and vysotu.Teper you know how to find the volume of a figure. This knowledge will be useful to geometry lessons at school, as this is the basis of solid geometry, also at the time the exam in mathematics. But remember! If all the known values you are in meters, and the volume of the figures obtained in cubic meters.

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## How to Find the Volume of a Cylinder?

While many would say that finding the area of a circle, rectangle, square and other 2-dimensional shapes is a piece of cake, the problem arises when you are dealing with 3-dimensional shapes.

A cylinder is a closed solid formed when two parallel, congruent circles are connected using a curved surface. How do you find the volume of a cylinder? Well, if you would like to know how then here are simple steps you need to follow.

**#1. Find The Radius Of The Circular Base**

Since the two circles at the two flat edges of a cylinder have the same radius, you only need to know the radii of only one of these. In case it is unknown, then the first option is to measure it using a ruler. If you know the diameter of the circle, then you can find the radius from it by dividing it by 2, since the radius is always half the diameter. The radius can also be derived if the circumference of the circle is known by using the formula, circumference = 2πr.

(Image Courtesy: Math Lab)

**#2. Find The Area Of The Circle**

Once you have successfully figured out the radius of the circle at the base, the next step is to calculate the area of the circle. You can conveniently measure it using the formula πr*r, where ‘r’ is the radius of the circle, and ‘π’ is a mathematical constant whose value is 3.14159 or 22/7. You do not necessarily have to calculate the exact value of the constant, and you can also leave the answer in terms of ‘π.’

**#3. Find The Height Of The Cylinder**

After finding the area of the circle at the base, now you need to know the height of the cylinder. The height of the cylinder is the distance between the edges of the two bases or the circles at the corner of the cylinder. In case you do not know it, then one way to measure it is using a ruler. Furthermore, if you know the curved surface area of the cylinder, then you can ascertain the cylinder’s height from it using the formula, curved surface area = 2πrh.

**#4. Multiply The Area Of The Circle With The Height Of The Cylinder**

Once you have calculated the area of the circle at the base as well as the height of the cylinder, what you need to do next is multiply the two, and you will get its volume. Think of the volume of the cylinder as the volume of the circle at the base stretching throughout the length or height of the cylinder. But since a circle is a 2-dimensional shape, its area is its volume. Therefore, multiplying the two with each other, you get the volume of the cylinder.

(Image Courtesy: Online Math Learning)

It is also important to note that volume is always calculated in cubic units, such as cubic cm, cubic inches, cubic feet and cubic meter. Also, always make sure that all your measurements are in the same unit before you start calculating the volume. So, if the radius and height are in other units, convert them into the same and then start your calculation.

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## How to Find the Radius of a Cylinder When Given the Volume and Height

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A cylinder is a three-dimensional object that looks like a rod with circular ends. If you know the volume of a cylinder and its height, you can determine its radius using the same formula used to calculate its volume when you do know the radius. Keep in mind that the radius is one half of the cylinder’s diameter, or the distance from the center of either end to its edge.

### 1. Know the Formula for the Volume of a Cylinder

The formula for the volume of a cylinder contains three elements: the radius of the cylinder (r), the height (h) of the cylinder, and the ratio of the circumference of a circle to its diameter *pi*. To find the volume of a cylinder, you multiply *pi* by the cylinder’s height and the square of its radius. Pi is approximately 3.14159 and can be rounded down to 3.14 if your calculator doesn’t have a pi key. Here is the formula in mathematical terms:

### 2. Solve for the Radius (r)

Since you want to find the radius of the cylinder, you need to rearrange the formula to solve for the term r, which is the radius. First, divide both sides by *pi* and h. These terms will cancel on the right side of the equation, leaving only r^2. Now take the square root of both sides to get rid of the square on the radius. This leaves us with the following:

r = square root of (V / (pi x h))

### 3. Calculate the Radius

Now just plug your numbers into the equation and compute the radius. For example, if your cylinder has a height of 10 centimeters and a volume of 30 cubic centimeters, the calculation would look like the following:

r = square root of (30 cm^3 / (3.14 x 10 cm)) = 0.98 cm

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