MENSURATION
Introduction : - This chapter deals with Measurments of
areas, volumes of triangles,
Rectangles, circles,
parallelogram, cubes etc..
Important formulas :
- Area of the rectangle =1/2 *base*height
- Area of equilateral triangle = √3/ 4 (side)²
- Semi perimeter of the triangle of sides a, b ,c is s= (a +b +c) / 2
- Area of the triangle = √(s(s-a)(s-b)(s-c))
- Area of the parallelogram = base * height
- Area of the rectangle = length*breadth
- Area of the square = (a)² = ½ (diagonal)²
- Diagonal = √2 a
- Perimeter = 4a
Trapezium : area =
½(sum of the parallel sides) * distance between them
Rhombus : area = ½
(product of diagonals)
Circle: area = ╥r², ╥
= 22/7 = 3.14
Circumference = 2╥r
Length of an area = 2╥r Ө / 360
Area of a sector = ╥r²Ө / 360
Volume and area of solid structure:
Cuboids: volume of the cuboid = l b h
Longest diagonal of the cuboid
= √ l²+b²+h²
Total surface
area = 2(lb+bh+lh)
Area of the room
(length * breadth)
Area of 4 walls
of the room = 2(l+b)*height
Cube:
Ø
Volume of the cube = a³
Ø
Longest diagonal = √3a
Ø
Total surface area = 6a²
Ø
Total length of all edges = 12a
Cylinder:
v
Volume = ╥r²h
v
Base area = ╥r²
v
Curved surface area = 2╥rh
v
Total surface area = 2╥rh+2╥r²
Pyramid: volume = 1/3
* area of the base * height
Cone: if the radius
of the base of the cone is r and height is h and slant height (l)
Then l²≠ h²+r²
·
Volume of the cone = ⅓ ╥ r²h
·
Area of the curved surface = ╥rl
·
Total surface area = ╥rl+╥r² = ╥r(l+r)
Sphere :
- Volume = 4/3 ╥r³ r-is the radius
- Curved surface area = 4╥r²
Hemi sphere:
·
Volume = 2/3 ╥r³
·
Curved surface area = 2 ╥r²
·
Total surface area = 3╥r²
·
Volume of spherical shell = 4/3 ╥(R³-r³)
·
Volume of the metal in a hallow pipe = ╥(R²-r²)h
·
Total surface area of an open pipe = 2╥[(Rh+rh+(R²-r²)]
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