Eduwhere's Concept: Volumes and Areas
In Mensuration, it is essential to be well versed with the formulae of the geometrical figures. Candidates can face questions related to the same in the Quantitative Aptitude section of their upcoming competitive examination.
Take a quick look at the important formulae for volumes and areas.
Area = S²
Perimeter = 4s
s = length of the sides, d = length of diagonal.
Area = ½ x base x height
Perimeter = x + y + z ( summation of three sides of a triangle)
Area = base x height = b x h
Perimeter = 2 (b + h)
Area = ½ x product of the diagonals between the sides * sine of the angle between the sides
Perimeter = 4 x side (any side)
Diagonal = 2 x area / diagonal
Area = ½ × sum of the parallel sides × height.
Area = product of any two sides x sine of the included angle
Perimeter = 2 (a + b) (a and b are the two adjacent sides)
Volumes of various solids:
In a cube, length = breadth = height = s
The surface area of a cube = 6s²
The volume of a cube = S³
Diagonal of a cube = √3 s
The curved surface area of a cylinder: 2 πrh( r = radius of the base, h = height)
The total surface area of a right circular cylinder = 2 πrh + 2 πr²
The volume of the right circular cylinder: πr²h
The surface area of a sphere: 4 πr²
The volume of a sphere: 4/3 πr³
A half-sphere is known as a hemisphere.
The curved surface area of a cone: pirl (l is the slant height)
The total surface area of a cone: πrl + πr²
The volume of a cone: 1/3 πr²h
Total surface area of a cuboid: 2 (lb + bh + lh)
The volume of a cuboid: lbh
The curved surface area of a hemisphere: 3 πr2
The total surface area of a hemisphere: 3 πr2
The volume of a hemisphere: 2/3 πr3