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Volume of Solids
SUMMARY
VIDEOS
REFERENCES
Solids:
Bodies that occupy space are called solids.
Solid bodies occur in various shapes, such as cuboid, cube, cylinder and cone.
Volume:
The space occupied by a solid body is called its volume.
The units for volume are cubic centimetre(cm3), cubic metre(m3) etc.
Cuboid:
A cuboid is a solid bounded by six rectangular plane faces.
Consider a cuboid of length, breadth and height are l,b and h respectively.
• Volume of cuboid = lbh cubic units
• Total surface area of cuboid = 2(lb + bh + lh)sq.units
• Lateral surface area of cuboid = Area of 4 walls = 2h(l + b)sq.units
Cube:
A cube whose length, breadth and height are all equal is called a cube.
Consider a cube of edge a units.
• Volume of cube = a3 cubic units
• Total surface area of cube = 6a2 sq.units
• Lateral surface area of cube = 4a2 sq.units
Cylinder:
A solid bounded by a cylindrical surface and two parallel circular bases at the top and bottom is called a cylinder.
Consider a cylinder of radius r units and height h units.
• Volume of cylinder = πr2h cubic units
• Total surface area of cylinder = 2πr( r + h) sq.units
• Lateral surface area of cylinder = 2πrh sq.units.
The volume of a cylinder is also sometimes known as its capacity.
Hollow cylinder
A solid bounded by two coaxial cylinders of the same height and different radii is called a hollow cylinder.
Surface area of each base = π(R2 - r2) sq.units
Curved surface area (CSA) = 2Ï€h(R + r) sq.units
Total surface area (TSA) = 2Ï€(R + r)(h + R - r) sq.units, where R = external radius, r = internal radius and h = height.
Volume (V) = πh(R2 - r2) cubic units.
Bodies that occupy space are called solids.
Solid bodies occur in various shapes, such as cuboid, cube, cylinder and cone.
Volume:
The space occupied by a solid body is called its volume.
The units for volume are cubic centimetre(cm3), cubic metre(m3) etc.
Cuboid:
A cuboid is a solid bounded by six rectangular plane faces.
Consider a cuboid of length, breadth and height are l,b and h respectively.
• Volume of cuboid = lbh cubic units
• Total surface area of cuboid = 2(lb + bh + lh)sq.units
• Lateral surface area of cuboid = Area of 4 walls = 2h(l + b)sq.units
Cube:
A cube whose length, breadth and height are all equal is called a cube.
Consider a cube of edge a units.
• Volume of cube = a3 cubic units
• Total surface area of cube = 6a2 sq.units
• Lateral surface area of cube = 4a2 sq.units
Cylinder:
A solid bounded by a cylindrical surface and two parallel circular bases at the top and bottom is called a cylinder.
Consider a cylinder of radius r units and height h units.
• Volume of cylinder = πr2h cubic units
• Total surface area of cylinder = 2πr( r + h) sq.units
• Lateral surface area of cylinder = 2πrh sq.units.
The volume of a cylinder is also sometimes known as its capacity.
Hollow cylinder
A solid bounded by two coaxial cylinders of the same height and different radii is called a hollow cylinder.
Surface area of each base = π(R2 - r2) sq.units
Curved surface area (CSA) = 2Ï€h(R + r) sq.units
Total surface area (TSA) = 2Ï€(R + r)(h + R - r) sq.units, where R = external radius, r = internal radius and h = height.
Volume (V) = πh(R2 - r2) cubic units.
SUMMARY
Solids:
Bodies that occupy space are called solids.
Solid bodies occur in various shapes, such as cuboid, cube, cylinder and cone.
Volume:
The space occupied by a solid body is called its volume.
The units for volume are cubic centimetre(cm3), cubic metre(m3) etc.
Cuboid:
A cuboid is a solid bounded by six rectangular plane faces.
Consider a cuboid of length, breadth and height are l,b and h respectively.
• Volume of cuboid = lbh cubic units
• Total surface area of cuboid = 2(lb + bh + lh)sq.units
• Lateral surface area of cuboid = Area of 4 walls = 2h(l + b)sq.units
Cube:
A cube whose length, breadth and height are all equal is called a cube.
Consider a cube of edge a units.
• Volume of cube = a3 cubic units
• Total surface area of cube = 6a2 sq.units
• Lateral surface area of cube = 4a2 sq.units
Cylinder:
A solid bounded by a cylindrical surface and two parallel circular bases at the top and bottom is called a cylinder.
Consider a cylinder of radius r units and height h units.
• Volume of cylinder = πr2h cubic units
• Total surface area of cylinder = 2πr( r + h) sq.units
• Lateral surface area of cylinder = 2πrh sq.units.
The volume of a cylinder is also sometimes known as its capacity.
Hollow cylinder
A solid bounded by two coaxial cylinders of the same height and different radii is called a hollow cylinder.
Surface area of each base = π(R2 - r2) sq.units
Curved surface area (CSA) = 2Ï€h(R + r) sq.units
Total surface area (TSA) = 2Ï€(R + r)(h + R - r) sq.units, where R = external radius, r = internal radius and h = height.
Volume (V) = πh(R2 - r2) cubic units.
Bodies that occupy space are called solids.
Solid bodies occur in various shapes, such as cuboid, cube, cylinder and cone.
Volume:
The space occupied by a solid body is called its volume.
The units for volume are cubic centimetre(cm3), cubic metre(m3) etc.
Cuboid:
A cuboid is a solid bounded by six rectangular plane faces.
Consider a cuboid of length, breadth and height are l,b and h respectively.
• Volume of cuboid = lbh cubic units
• Total surface area of cuboid = 2(lb + bh + lh)sq.units
• Lateral surface area of cuboid = Area of 4 walls = 2h(l + b)sq.units
Cube:
A cube whose length, breadth and height are all equal is called a cube.
Consider a cube of edge a units.
• Volume of cube = a3 cubic units
• Total surface area of cube = 6a2 sq.units
• Lateral surface area of cube = 4a2 sq.units
Cylinder:
A solid bounded by a cylindrical surface and two parallel circular bases at the top and bottom is called a cylinder.
Consider a cylinder of radius r units and height h units.
• Volume of cylinder = πr2h cubic units
• Total surface area of cylinder = 2πr( r + h) sq.units
• Lateral surface area of cylinder = 2πrh sq.units.
The volume of a cylinder is also sometimes known as its capacity.
Hollow cylinder
A solid bounded by two coaxial cylinders of the same height and different radii is called a hollow cylinder.
Surface area of each base = π(R2 - r2) sq.units
Curved surface area (CSA) = 2Ï€h(R + r) sq.units
Total surface area (TSA) = 2Ï€(R + r)(h + R - r) sq.units, where R = external radius, r = internal radius and h = height.
Volume (V) = πh(R2 - r2) cubic units.
