Cylinder – the stereometric geometrical figure formed by rotation of a rectangle around one of its parties, and having circles in the bases. The piece of a wire, a tube can be a physical example of a cylinder. To determine the volume of a cylindrical body, it is necessary to define at first, it has cylinder what appearance.
Instruction
1. If this body has a usual cylinder, then its volume is as the work of height on the area of the basis. The basis at such cylinder is the circle which area pays off as the work of number "пи" on a square of radius or the relation of the work of number "пи" on diameter square to four. S=π * (R) in a square or S=π* (D) in a square/4. Then the volume of a full cylinder is calculated by a formula: V = h *π * (R) in a square or V = h * π * (D) in a square/4. Example 1. It is necessary to find cylinder volume if the radius of its basis is equal to 15 cm, and its height of 10 cm. Decision 1: V = h *π * (R) in a square = 10 sm*3.14*15*15 = 7065 cubic see Decision 2: Knowing that diameter is twice more than radius, to find diameter: D = 2*15sm = 30 cm. And then, V = h * π * (D) in a square/4 = 10sm*3,14*30*30/4=7065 cubic see.
2. Other type of a cylinder is called a hollow cylinder, an empty cylinder or a pipe. Its volume is more difficult, considering more irregular geometrical shape of such figure (see the drawing). If to enter designations: R – radius of a big circle of the basis, r is the radius of a small circle of the basis, h is the cylinder height then the volume of a pipe is calculated by a formula: V = π * ((R) in a square – (r) in a square) *h. Example 2. Let it is necessary to find the volume of a hollow cylinder 1 m high if the external circle has the radius of 0.5 m, and internal – 0.1 m. Decision: V = π * ((R) in a square – (r) in a square) *h = 3.14*1m (0.5m*0.5m – 0.1m*0.1m) =0.75 cubic meters.
3. If in hollow the formula of volume of a pipe takes the following form: V = πh/4 (D in a square – d in a square). Example 3. Diameter of a big circle of the basis of a cylinder is equal to 25 cm, small – 20 cm. To find the volume of such pipe if its height – 15 cm. Decision: V = πh/4 (D in a square – d in a square) = 3.14*15см/4(625см-400см) =2649 cubic centimeters.