Advice 1: How to find the mass of the cylinder

The mass of any physical object helps to assess what force must be applied to move it in the absence of gravity and friction forces. But we often have to deal with the mass in another form, usually called "weight". It is defined as the force with which the physical body presses on the surface under the influence of gravity. To distinguish between these two forms of the mass are called "inertial" and "gravitational".
How to find the mass of the cylinder
Weigh the cylinder with weights desired degree of accuracy and get the value of its mass in terms of exposure to earth's gravity - the gravitational mass. This is the easiest, but not always available method applicable to physical objects not only of cylindrical shape.
If possible weigh not, then calculate the amount of space which is a cylindrical object and determine the density of the material of which it is composed. These two features are associated with a constant mass ratio, the formula which will calculate body mass. For determining the density of a substance will have to use relevant tables from the guides. In the paper version you can rent them in the library and in electronic form - find online or in the store on optical disks with thematic collections.
The volume of a cylinder you can determine the means at hand - for example, immerse it in the water-filled volumetric glassware, and assess the volume of displaced water. The value obtained is likely to be marked on the measuring instruments in liters and derived units. For payment in cubic meters and its derivatives use this ratio: one liter equal to one cubic decimeter.
If you define a volume (V) given in the previous step by the way is not possible, then determine the physical dimensions of the cylinder diameter (d) and height (h). Calculate the value of one quarter of the works of PI, taken with the necessary degree of precision on the squared diameter to find the area of the base of the cylinder. Multiply it by the height and get the volume of a cylindrical object is: V=¼*π*d*h.
Now you know the density (ρ), which comprises the cylinder, and its volume (V). To calculate the mass (m) of the object just multiply the two values: m=ρ*V.

Advice 2: How to find the volume of a cylinder

A cylinder is called a geometric solid formed by a cylindrical surface bounded by two parallel planes. The cylinder obtained by rotating a rectangle around any of its sides is called a straight. With just a few simple methods you can quite accurately find the volume of a cylinder.
Direct cylinder
You will need
  • • Ruler or tape measure.
  • • A pencil or marker.
  • • A sheet of paper or cardboard or other suitable object with right angles.
Suppose you have a water tank of cylindrical shape. You need to fill it with water, but you want to calculate the volume that it will fill.

From the school course of geometry you know that the formula of volume of cylinder is:

V = SH ,

that means, the volume of a cylinder equals the area of S is at its height H.

The height of the cylinder H to easily measure a tape measure or ruler.
Determine the height of the cylinder
Now, define the footprint. The area of a circle, as we know from school the geometry is determined by the formula:

S = πR2,

where π is the digit in mathematics the ratio of the lengths of the circumference and the diameter and is equal to 3.14159265...,

and R is the radius of the circle

How to calculate the area of a circle with only a ruler? Very simple!

From the same school course of geometry recall that any circle can be inscribed right triangle. Moreover, the hypotenuse of this triangle is equal to the diameter of the circle.

To do this, take a piece of cardboard or other suitable object having angles and imposed on our cylinder so that a right angle α with its tip And rests against the edge of the cylinder.
Fit the cylinder right triangle
Side of the rectangle that are intersected by the circle, mark it with a pencil or marker and connect with a straight line. In our case, the vertices of the triangle b and C. This cut is the diameter of our circle. The radius of the circle is equal to half its diameter. Divide the segment BC into two parts. The center of the circle is point O. the Segments Ob and OC are equal and are the base radius of the cylinder. Now substitute the obtained values into the formula:

V = πR2H
Defined by the base radius of the cylinder
If you can measure the parameters of your cylinder in inches, the result will be in cubic centimeters (cm3). If the measurements are taken in metres, the result will be, respectively, obtained in cubic metres (m3).
Useful advice
If you must convert cubic inches to liters of volume, then multiply the result by 0, 001, this is the volume of the cylinder in litres. If your result will be calculated in cubic meters, then multiply it by 1000. For example: you got in the result of measurements and calculations volume 0, 5 m3. Liters it will be 0, 5 x 1000= 500 litres.

Advice 3: How to find the volume of a cylinder

Cylinder – stereometric geometrical figure formed by the rotation of a rectangle about one of its sides, and having at the base circles. A physical example of a cylinder can be a piece of wire, tube. To determine the volume of a cylindrical body, one must first determine what kind of cylinder it has.
How to find the volume of a cylinder
If the body has the usual cylinder, its volume is the product of the height of the square base. The basis of such cylinder is a circle, whose area is calculated as the product of "PI" to the square of the radius or the ratio of product of "PI" to the square of the diameter by four. S=π *(R) squared, or S=π* (D) squared /4. Then the volume of the full cylinder is calculated by the formula: V = h *π *(R)squared or V = h * π * (D) squared /4. Example 1. Need to find the volume of a cylinderif the radius of its base is equal to 15cm, and the height is 10 cm. Solution 1: V = h *π *(R) squared = 10 cm*3,14*15*15 = 7065 cubic cm Solution 2: Knowing that the diameter is twice the radius, find the diameter : D = 2*15cm = 30cm. Then, V = h * π * (D) squared /4 = 10cm*3,14*30*30/4=7065 cubic cm
Another kind of cylinder is called a hollow cylinder, empty cylinder or tube. It is harder, given more complex geometric shape such figure (see figure). If we introduce notations: R is the radius of the large circle of the base, r is the radius of the small circle of the base, h is the height of the cylinder, then the volume of the pipe is calculated by the formula: V = π *( (R) squared is (r) squared)*h. Example 2. May need to find the volume of a hollow cylinder with a height of 1 m if the outer circle has a radius of 0.5 m, and the inner – 0.1 m. Solution: V = π *( (R) squared is (r) squared)*h = 3,14*1m(0.5 m*0.5 m – 0.1 m*0.1 m)=0,75 cubic meter.
If in a hollow cylinder to consider the external and internal diameters, introducing the notation: D is the diameter of a great circle d – diameter of the small circle, the formula for the volume of the pipe will be as follows: V= πh/4 (D squared – d squared).Example 3. The diameter of the large circle of the base of the cylinder is equal to 25 cm, small – 20 cm. Find the volume of this pipe, if its height is 15 cm Solution: V= πh/4 (D squared – d squared)= 3,14*15cm/4(625см-400cm)=2649 cubic centimeters.
Useful advice
Often when solving geometric tasks, the number "PI" is allowed to take the value equal to the number three.
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