You will need
- measuring tools;
Use for calculating volume of a cylinder formula:V = H x S, where V is the volume of the cylinder; H-height; S – the area of one of the bases; x is a multiplication sign.This formula can be applied only in the case when the footprint is known from the conditions of the problem and requires no prior calculations. For example, if the height of the cylinder is 2 m and the area of one of its bases is equal to 3.5 m, then V = 2 x 3.5 = 7 cubic meters.
If the footprint of unknown conditions previously perform a calculation. For this construct in the square is known or measured the radius of the circle lying at the base, and multiply it by the number "PI" equal approximately to 3.14. For example, if the radius is 1.2 m, the footprint is: S = 1.2 x 1.2 x 3,14 = of 4.52 sq. m. Now multiply the value by the height of the cylinderto get volume.
In the case of known diameter of the cylinder and height calculate the volume of geometric solids according to the formula:V = 3,14 x H x D2 / 4, where V is the volume of the cylinder; 3,14 – the PI; H – height of cylinder; D – diameter; x – multiplication; / – division sign.So if the diameter of the circle lying at the base is 0.5 m, the height of the cylinder is 1.2 m, the volume will be: 3,14 x 1.2 x 0.5 x 0.5 / 4 = of 0.236 cubic meters.
At a known length of the circumference of the base and height find the volume of the cylinder as the product of the height of the cylinder to the quotient of the square of the circumference by the following formula:V = x L2 H / (3,14 x 4), where V is the volume of the cylinder; 3,14 – the PI; H – height of the cylinder; L is the length of the circle lying at the base of the cylinder.
If you need to measure the real volume of the cylinder, before carrying out calculations for one of the above formulas produce a measurement of the object by means of measuring instruments. To measure the linear parameters of the geometric body use a ruler, calipers, measuring cord or tape.
Apply the principle of copying, if to measure parameters of the cylinder in place is not possible. To do this, take a picture of the cylinder, including its base and height, by placing next to a ruler or object of known size, e.g. a matchbox. Then measure the size of photographs, transferring the data at the appropriate scale.
Advice 2: How to find the volume of a cylinder
Cylinder refers to three-dimensional geometric shapes, the so-called solids of revolution. Its bases are equal circles. The cylinder can be straight and inclined.
You will need
- — the range;
In that case, if you know the area of at least one of the bases of the cylinder (they are equal), measure its height. To do this, drop a perpendicular from one base cylinder on to another, and measure its length. The height of the straight cylinder is equal to any of the sides. Then find the volume by multiplying the area of one of the bases of the cylinder S to the height h (V=S∙h). For example, if you know that the area of the circle lying at the base of the cylinder is 8 cm2 and its height is 5 cm, then its volume is V=8∙5=40 cm3.
In that case, if the base area of the cylinder is unknown, its volume can be found using another formula. Measure the height of the cylinder in any convenient way. Then, find the diameter of the base of the cylinderby measuring its convenient way, for example, using a ruler or calipers. Calculate the radius of the cylinderby dividing the diameter by 2. Find the volume of this geometric body by multiplying the number π≈3,14 the square of the radius R and the height of the cylinder h (V= π∙R2∙h).
Example.Find the volume of a cylinder, whose base has a diameter of 6 cm and the height is 5 cm Determine the base radius of the cylinder R=6/2=3 cm Calculate the volume V= 3,14∙32∙5=141,3 cm3.
If the cylinder is inclined, the above formula remains valid, but the height in this case is not equal to the generatrix. Therefore, in order to find the volume, measure the length of the generatrix l, and multiply it by the area of the base S, which can be found as described above, and the sine of the angle α between the generatrix and the plane of the base V=S∙l∙sin(α).
Example. Forming a circular cylinder has a length of 16 cm and is at an angle of 45 ° to the base. Find the volume of a cylinderif the base radius is 8 cm First, find the area of the base of the cylinder. It is equal to S=π∙R2. Substitute the value of this formula in the expression for the volume and get V= π∙R2∙l∙sin(α)=3,14∙82∙16∙sin(45°)≈2273,6 cm3.