Volume of Cylinder : In the case of a right circular cylinder, the volume or capacity is the product of the base area and height.
The line joining the centers of the circles is called the axis of the cylinder. If the axis is perpendicular to the base then the cylinder is called the right circular cylinder.
The formula to find the Volume of Cylinder is :
Volume of Cylinder = π r^{2} h
Volume of a hollow cylinder = πR^{2} h - π r^{2} h
Some solved examples :
1) The trunk of a tree is cylindrical and its circumference is 176 cm. If the length of the trunk is 3 m, find the volume of the timber that can be obtained from the trunk. Solution : Circumference = C = 176 cm ; length = h = 3 m = 300 cm
∴ 2 π r = 176
⇒ r = 176 / 2 π
⇒ r = 176 / 6.28 ( taking π = 3.14)
∴ r = 28.02 = 28 cm
Volume = π r^{2} h
V = 3.14 x 28 x 28 x 300
V = 738528 cm^{3}
V = 0.738528 = 0.74 m^{3}
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2) The volume of a metallic cylindrical pipe is 1408 cu.cm. Its length is 14 cm and its external radius is 9 cm. Find its thickness. Solution : Here, R = external radius of the pipe = 9 cm.
h = length of the pipe = 14 cm
V = volume of the pipe = 1408 cu.cm
Let r be the internal radius.
Now, V = π R^{2} h - π r^{2} h
V = π ( R^{2} - r^{2}) x h
⇒ 1408 = 3.14 ( 9^{2} - r^{2}) x 14
⇒ 1408 = 43.96 ( 81 - r^{2})
⇒ 1408 / 43.96 = 81 - r^{2}
⇒ 32 = 81 - r^{2}
⇒ r^{2} = 81 – 32
⇒ r^{2} = 49
⇒ r = 7 cm
∴ Thickness of the pipe = R – r = 9 – 7 = 2 cm.
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3) How many bags of wheat can be emptied into a circular container of height 1.75 m and base radius 4.2 cm, if the space required by each bag of wheat is 2.1 cu.m ? Solution : Here, r = 4.2 m ; h = 1.75 m
Volume of a circular container = π r^{2} h
= 3.14 x 4.2 x 4.2 x 1.75
= 96.93 cu.m
Volume of each bag = 2.1 cu.m
∴ Number of bags = (volume of container) / Volume of bag of wheat
= 96.93 / 2.1 = 46.15
= 46 ( full bags). Volume :