SSC TRICKS FOR MATHS

CUBE d = side VOLUME : V = d^2 SURFACE AREA : S = 6(d^2) RECTANGULAR SOLID l = length, w = width, h = height VOLUME: V = lwh SURFACE AREA : S = 2lw + 2lh + 2wh SPHERE r = radius VOLUME : V = 4/3*pi*r^3 SURFACE AREA : S = 4*pi*r^2 RIGHT CIRCULAR CYLINDER r = radius, h = height VOLUME : V = pi*r^2*h SURFACE AREA : S = 2*pi*r*h + 2 *pi*r^2 TORUS r = tube radius, R = torus radius VOLUME : V = 2*pi^2*r^2*R SURFACE AREA : S = 4*pi^2*r*R PYRAMID A = area of base , h = height VOLUME : V = 1/3*A*h RIGHT CIRCULAR CONE r = radius, h = height VOLUME : V = 1/3*pi*r^2*h SURFACE AREA : S = pi*r*[sqrt(r^2 + h^2)] + pi*r^2 FRUSTUM OF A CONE r = radius, R = base radius, h = height, s = slant height VOLUME : V = pi/3(r^2 + rR + R^2)h SURFACE AREA : S = pi*s(R+r) + pi*r^2 + pi*R^2 SQUARE PYRAMID s = side, h = height VOLUME : V = ...

SOME RESULTS ON CIRCLES THEOREM 1. IF TWO ARCS OF A CIRCLE ARE CONGRUENT THEN THE CORRESPONDING CHORDS ARE EQUAL. THEOREM 2. THE PERPENDICULAR FROM THE CENTRE OF A CIRCLE TO A CHORD BISECT THE CHORD. THEOREM 3.  THE LINE JOINING THE CENTRE TO THE MID POINT OF A CHORD IS PERPENDICULAR TO THE CHORD. THEOREM 4.  THE PERPENDICULAR BISECTORS OF THE CHORDS OF A CIRCLE INTERSECT AT ITS CENTRE. THEOREM 5.  THERE IS ONE AND ONLY ONE CIRCLE PASSING THROUGH THREE NON COLLINEAR POINTS. (I) AN INFINITE NUMBER OF CIRCLE CAN BE DRAWN TO PASS THROUGH A SINGLE POINT. (II) AN INFINITE NUMBER OF CIRCLE CAN BE DRAWN TO PASS THROUGH TWO GIVEN POINTS. (III) A UNIQUE CIRCLE CAN BE DRAWN TO PASS THROUGH THREE GIVEN NON COLLINEAR POINTS. THEOREM 6.  EQUAL CHORDS OF CONGRUENT CIRCLES ARE EQUIDISTANT FROM THE CORRESPONDING CENTRES ARE EQUAL. THEOREM 7. CHORDS WHICH ARE EQUIDISTANT FROM THE CORRESPONDING CENTRES ARE EQUAL. THEOREM 8.  EQUAL CHORDS OF A ...