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.
Often when solving geometric tasks, the number "PI" is allowed to take the value equal to the number three.