Volume of a CylinderIn this section, we will learn the formula of the volume of a cylinder and how to find the volume of a cylinder along with proper examples. A cylinder is a 3D geometrical shape with the twocircular base. It has two circular bases, one at top and the other at the bottom. We can also define a cylinder as an arrangement of circular disks in stacked form. There are two types of cylinders:
DefinitionThe number of cubic units that will exactly fill a cylinder is called the volume of the cylinder. In other words, the space covered by a cylinder is called the volume of a cylinder. The Volume of Cylinder FormulaIt is the product of the area of base and height of the cylinder.
V=πr^{2} h
Volume of a Hollow CylinderA cylinder that is hollow from inside is called a hollow cylinder. There are two radii in the hollow cylinder. One for the inner cylinder and the other for an outer cylinder formed by the base. Suppose, r_{1} is the radius of the outer circle, r_{2} is the radius of the inner circle, and h is the height of the cylinder, then the volume of the hollow cylinder will be: How to Find Volume of a CylinderWe can find the volume of a cylinder by multiplying the area of a circle by the height of the cylinder. We know the formula of the area of a circle: The Area of a Circle (A)= πr^{2} Multiply the area of a circle by the height of the cylinder, we get the volume of the cylinder. Since,
The Volume of a Cylinder (V)= πr^{2} h
Where: π: It is a constant whose value is 3.142 or 22/7. r: It is the radius of the cylinder. h: It is the height of the cylinder. Note: The radius and height must be in the same unit. Convert the units if they are different.Unit of VolumeThe unit of the volume is a cubic unit or unit^{3}. For example, if the radius and height are given in centimeters, the volume will also in centimeters, and the unit will be cubic centimeters or cm^{3}. Let's see some examples. Example 1: The radius of a cylinder is 5 cm, and the height is 12 cm. Calculate the volume of the cylinder. Take π=. Solution: Given, radius (r) = 5 cm Height (h) = 12 cm π= Volume (V) =? We know the formula of volume of a cylinder: V= πr^{2} h Putting the values in the above formula, we get: Hence, the volume of the cylinder is 942.85 cm^{3}. Example 2: Calculate the volume of a cylinder whose radius is 3 cm and the height is 6 cm. (π=3.14) Solution: Given, radius (r) = 3 cm Height (h) = 6 cm π=3.14 Volume (V) =? We know the formula of volume of a cylinder: V= πr^{2} h Putting the values in the above formula, we get: V=3.14×(3^{2})×6 Hence, the volume of the cylinder is 169.56 cm3. Example 3: What is the volume of the cylinder given below. Solution: Given, radius (r) = 4.5 cm Height (h) = 8 cm Volume (V) =? We know the formula of volume of a cylinder: V= πr^{2} h Putting the values in the above formula, we get: V=3.14×(4.5^{2})×8 Hence, the volume of the cylinder is 508.68 cm^{3}. Example 4: The volume of a cylinder is 255 cm^{3} and the height is 15 cm. Find the radius (r) of the cylinder. Solution: Given, Volume (V) = 255 cm^{3} Height (h) = 15 cm π=3.14 Radius (r) =? We know the formula of volume of a cylinder: V= πr^{2} h Putting the values in the above formula, we get: Hence, the radius of the cylinder is 2.3 cm. Example 5: Find the volume of the hollow cylinder. Solution: Given, radius of outer cylinder (r_{1}) = 2.4 cm radius of inner cylinder (r_{2}) = 2 cm Height (h) = 10 cm π=3.14 Volume (V) =? We know the formula of volume of the hollow cylinder: Putting the values in the above formula, we get: V=3.14×10×(2.4^{222) V=3.14×10×(5.764) V=3.14×10×(1.76) V=55.264} Hence, the volume of the hollow cylinder is 55.264 cm^{3}. Example 6: The outer and inner radius of a pipe is 8 and 6 cm, respectively. The height of the pipe is 15 cm. Find the volume of the pipe. Take pi=3.14. Solution: Given, radius of outer cylinder (r_{1}) = 8 cm radius of inner cylinder (r_{2}) = 6 cm Height (h) = 15 cm π=3.14 Volume (V) =? We know the formula of volume of the hollow cylinder: Putting the values in the above formula, we get: V=3.14×15×(8^{2}6^{2}) Hence, the volume of the hollow cylinder is 1318.8 cm^{3}.
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