Step-by-step explanation:
Volume of a Cylinder:
In geometry, a cylinder is a three-dimensional shape with a circular base, a circular top and straight sides. It is the solid figure that you get when you rotate a rectangle about one of its sides. In most cases when we talk about the volume of a cylinder, we are talking about how much liquid it can hold.
The strictly correct way of saying it is "the volume surrounded by a cylinder" - the amount of liquid it holds. But many textbooks simply tell "the volume of a cylinder" to mean the same thing.
Remember that the radius and the height must be in the same units - convert them if necessary.
The resulting volume will be in those cubic units. So if the height and radius are both in centimeters, then the volume will be in cubic centimeters.
The volume of a cylinder is found by multiplying the area of its top or base by its height and is defined as: V = π· r2· h
Example 1: A cylindrical water storage tank has an inside base radius of 7m and depth of 11 m. Find the capacity of the tank in kiloliters (1kl = 1m3).
Solution:
Base radius: r = 7 m
Height: h = 11 m
The water storage tank is in the shape of the cylinder. So using the volume of cylinder formula we can find the volume of it.
V = π· r2· h
V = π· 72· 11
V = 1692.46 m3 = 1692.46 kl
Example 2: Find the volume of a cylinder whose base radius is 6 cm and height is 4 cm.
Solution:
Base radius: r = 6 cm
Height: h = 4 cm
V = π· r2· h
V = 3.14· 62· 4
V = 452.16 cm3
Example 3: If the capacity of a cylindrical tank is 1848 m3 and the diameter of its base is 14 m, find the depth of the tank.
Solution:
Let the depth of the tank be h metres. Then we have:
V = π· r2· h
h = V / π· r2
h = 12 m
Example 4: A conical vessel, whose internal radius and height is 20cm and 50 cm respectively, is full of liquid. Find the height of the liquid if it is put into a cylinder whose base radius is 10 cm.
Solution:
The volume of the vessel is:
V = π ∙ r2 ∙ h / 3
V = π · 202· 50 / 3
V = 20944 cm3
The volume of the liquid is the same no matter it is in the vessel or in the cylinder, therefore we have:
V1 = V2, where V1 is the volume of the vessel and V2 is the volume determined using the formula for a cylinder.
20944 = π · 102 · h
Thus:
h = 20944 / (π · 102)
h = 66.67 cm
Example 5: Find the volume of a right circular cylinder whose curved surface area is 2640 cm2
And the circumference of its base is 66 cm.
Solution:
To begin with we need to determine the base radius using the formula for circular perimeter (circumference).
P = 2 · π ·r
r = P /(2 · π) = 66 / (2 · π) = 10.50 cm
Now we will find the height of the cylinder using the formula for surface area of a cylinder.
SA = P · h
h = SA / P = 2640 / 66 = 40 cm
The volume of the cylinder is therefore:
V = π· r2· h
V = π· 10.502· 40
V =13854.4 cm3
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