CONTENT LIST
Volume and Surface area of Solid
Solid
The object having definite shape and size are called solid.
A solid occupies a definite shape.
Things to remember
Total surface area: The total surface area of an object is sum of area of all of the surfaces of the object.
Lateral surface area: The lateral surface area of an object is equal to area of all of the sides of the object, except its base and top.
Curved surface area: The curved surface area of an object is equal to area of curved surface of the object.
Cuboid
Solids like matchbox, chalkbox, a tile, a book, an almirah, a room, etc., are in the shape of a cuboid.
Formulae for cuboid
length = l, breadth = b , height = h
i) Volume = l x b x h
ii) Total surface area = 2(lb + bh + lh)
iii) Lateral surface area = 2(l + b) x h
iv) Diagonal = √(l² + b² + h²)
Cube
Solids like ice cube, sugar cube, dice, etc., are in the shape of a cube.
Formulae for cube
length of each side = a
i) Volume = a³
ii) Total surface area = 6a²
iii) Lateral surface area = 4a²
iv) Diagonal = (√3)a
Cylinder
Solids like jars, water bottle, pvc pipe, tumbler, etc., are in the shape of a cylinder.
Formulae for cylinder
radius = r, height = h
i) Volume = πr²h
ii) Total surface area = 2πr(h + r)
iii) Curved surface area = 2πrh
Hollow Cylinder
Solids like iron pipes, rubber tubes, pvc pipe, etc., are in the shape of a hollow cylinder.
Formulae for hollow cylinder
internal radius = r, external radius = R, height = h
i) Volume = πh(R² - r²)
ii) Total surface area = 2π(R + r)(h + R - r)
iii) Curved surface area = 2πh(R + r)
Cone
Solids like ice-cream cone, conical tent, funnels, etc., are in the shape of a cone.
Formulae for cone
radius = r, height = h, slant height = l = √(h² + r²)
i) Volume = (1/3)πr²h
ii) Total surface area = πr(l + r)
iii) Curved surface area = πrl
Sphere
Solids like football, cricket ball, etc., are in the shape of a sphere.
Formulae for sphere
radius = r
i) Volume = (4/3)πr³
ii) Surface area = 4πr²
Hemisphere
Solids which are half of sphere is known as hemisphere.
Formulae for hemisphere
radius = r
i) Volume = (2/3)πr³
ii) Curved surface area = 2πr²
ii) Total Surface area = 3πr²
Spherical shell
Formulae for spherical shell
internal radius = r, external radius = R
i) Volume = (4/3)π(R³ - r³)
