Friday, October 26, 2007

MENSURATIONS

MENSURATIONS


1. Square:-figure


(1)Area = a2Sq units.

(or)


P2/16


(2)Perimeter = P =4a

(or)


a = P/4


(3)Digonal

(or)length of the rod that can be placed=




a = P/4




2.Rectangle:-figure


(1)Area =


l*b


(2)Perimeter = P =


2(l+b)


(3)Digonal =


d = Öl2+b2


Þb = Öd2-l2
Þl = Öd2-b2

3.If area of plot is given as 'z'm2 and the
ratio of l:b is given as x:y, then length is





l = x * [Öz/(x*y)]


b = y * [Öz/(x*y)]





4.


length required=(length * breadth of a room)/width of the carpet




5.


No:of stones =(length * breadth of a room)/(length * breadth of a stone)




6.


A2/A1= (a2/a1)2 = (d2/d1)2




7.


P2/P1=ÖA2/A1




8.Circle:-figure


(1)Area =


Pr2 (or) P(d2/4)


(2)


d = 2r


(3)Perimeter (or) Circumference =





2Pr = Pd


Where P = 22/7 (or) 3.14
(4)


A = c2/(4 P) (or) c = Ö4 PA = 2ÖPA




9. % dec in Area =




fs [(r12 - r22)/r12] * 100




10. Distance travelled in 'N' revolutions is,




D = N * Pd (or) N = D/(Pd)




11.Area left ungrazed =




a2(1 - P/4)




12.Road out of the garden:-figure


(1)Area of the road =




2w[l+b+2w] = [(l+2w)(b+2w)]-(l*b)


Road inside the garden:-figure

(2)Area of the road =




2w[(l+b)-2w]


Two parallel roads:-figure


(3)Area of the road =





w[(l+b)-w]




13.Traingles:-


(1)Right angled traingles:-figure

Area = (1/2)*b*h


d = Öb2+h2


(2)Equilateral traingles:-figure

Area=


(Ö3/4)a2


Perimeter = P =


3a


Height=


(Ö3/2)a



(3)Scalene traingle:-figure


Perimeter = P =


2s=a+b+c


Þs=(a+b+c)/2


Area =


Ös(s-a)(s-b(s-c)


(4)Isosceles traingle:-figure

Perimeter = P


2a+b


Area =


b/4(Ö4a2-b2)




14.Volumes:-
(a)Cube:-figure

(1)Lateral surface area =




4a2


(2)Total surface area =




6a2


(3)Volume of a solid = Base area * Height =




a2 * a = a3


(4)Diagonal (or) Longest pole = d =




Ö3a




(b)Cuboid:-figure

(1)Lateral surface area = AL =




2h[l+b]


(2)Total surface area = AT




2[lb+lh+bh]


(3)Volume = V =




lbh


(4)Diagonal = d =




Öl2+b2+h2




(5)No:of boxes =




(lbh)/l1b1h1 = (Volume of big box)/(Volume of small box)




15.


a3 = v13+v23+v33




16.


a1/a2 = (v1/v2)1/3




17.No:of boxes(if areas are given) =




a3/a13 = (a/a1)3




(18)Cylinder:-figure

(1)Lateral surface area = AL =


2Prh


(2)Total surface area = AT


2Pr(h+r)


(3)


AT/Al=(h+r)/h


(4)Volume = v =


Pr2h


(5)Area of each flat surface i.e of ends =


Pr2




(19)Cone:-figure

(1)Slant height = L =


Öh2+r2


(2)Volume of the cone =


1/3(Pr2h)


(3)Curved surface area of cone =


Prl


(4)Total surface area =


Pr(l+r)


(5)


v1/v2=(r1/r2)2 * h1/h2




20.


H-h = (4/3) * rs 3/rd2




21.Area of circle inscribed in an equilateral
traingle is r2.It's height is,




h = 3r




(22)Sector:-figure

(1)


l= (q/360)*2P r


(2)A =


(q/360)*Pr2


(3)Circumference,c =




l+2r




(23)Four circular carboard pieces,each of radius 'r'cm
are placed in such a way that each piece touches two
other pieces.The area of the space enclosed by four
pieces is,


(2r)2 [1-P/4]cm2




(24)Rhombus:-figure

(1)


4a2 = d12 + d22


(2)Area =


(1/2)d1d2


(3)Perimeter = P =


4a




(25)Parallelogram:-figure

(1)Area of DleABC




1/2(bh)


(2)Area of DleACD




1/2(b/h)


(3)Area of parallelogram =




bh




(26)Trapezium:-figure

(1)Area of Trapezium=Area of (DleABC + DleACD)




1/2(ah) + 1/2(bh) = [(1/2)h][a + b]




(27)Sphere:-figure

(1)Surface area =


4Pr2


(2)Volume =


4/3(Pr3)


(3)


A1/A2 = (r1/r2)2


(4)


v1/v2 = (r1/r2)3


(5)


v1/v2 = (A1/A2)3/2


(6)


A1/A2 = (v1/v2)2/3




28.Area of four walls =




2 * (length + breadth) * height


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