# Area and Volumes

Area of a rectangle = Length x Breadth

(Diagonal)^{2} = (Length)^{2} + (Breadth)^{2}

Area of a square = (side)^{2} = (½) (Diagonal)^{2}

Area of 4 walls of a room = 2 (Length + Breadth) x Height

Area of a parallelogram = (Base x Height)

Area of a rhombus = (½) (product of diagonals)

When d_{1} and d_{2} are the two diagonals then side of rhombus

= (½) √d_{1}^{2} + d_{2}^{2}

Area of an equilateral triangle = (√3/4) (side)^{2}

If a, b, c are the lengths of the sides of a triangle and

S = (½) (a + b + c), then :

Area of the triangle = √s(s-a) (s-b) (s-c)

Area of a triangle = (½) x Base x Height

Area of a trapezium = (½) (sum of parallel sides x distance between them)

Circumference of a circle = 2 л r

Area of a circle = л r^{2}

Arc AB = (2 л r Ө)/360^{o} , where angle AOB = Ө and O is the centre

Area of sector AOB = (л r^{2} Ө)/360^{o}

Area of sector AOB = (½) (arc AB) r

Cuboid : Let length = l, breadth = b and height = h units

volume of cuboid = (lbh) cubic units

whole surface of cuboid = 2 (lb + bh + lh) sq. units

diagonal of cuboid = √l^{2} + b^{2} + h^{2} units

Cube : Let each edge (or side) of a cube be a units. Then :

volume of the cube = a^{3} cubic units

whole surface of the cube = (6a^{2}) sq. units

diagonal of the cube = (√3a) units

Cylinder : Let the radius of the base of a cylinder be r units and its height (or length) be h units. Then :

volume of the cylinder = (л r^{2} h) cu. units

curved surface area of the cylinder = (2 лrh) sq. units

total surface area of the cylinder = (2 л rh + 2 л r^{2}) sq. units

Sphere : Le the radius of a sphere be r units. Then :

volume of the sphere = (4/3) л r^{3} cu. units

surface area of the sphere = (4 л r^{2}) sq. units

volume of a hemisphere = (2/3) л r^{3} cu. units

curved surface area of the hemisphere = (2 л r^{2}) sq. units

whole surface area of the hemisphere = (3 л r^{2}) sq. units

Cone : Let r be the radius of the base, h the height and l the slant height of a cone. Then :

slant height l = √h^{2} + r^{2}

volume of the cone = (1/3) л r^{2} h cu. units

curved surface area of the cone = (лrl) sq. units = (л r √r^{2} + h^{2}) sq. units

total surface area of the cone = (л rl + л r^{2})