If 'r' is the radius, 'x' is the
diameter, 'P' is the perimeter (or circumference) and 'A' is the area of a circle then
(i) x = 2r
(ii) P = 2πr or P = πx
(iii) A = πr2 or A = (πx2/4)
(2) Sector :
If 'r' is the radius, 'l' is the
length of the arc and 'θ' is the angle, 'P' is the perimeter and 'A' is the area of a
sector, then
(i) l = rθ
(ii) P = l + 2r
or P = rθ + 2r = r(θ + 2)
(iii) A = l r
or A = r2θ
(3) Cube :
If 'x' is the side, 'S' is the surface
area and 'V' is the volume of a cube,
then
(i) S = 6x2
(ii) V = x3
(4) Sphere :
If 'r' is the radius, 'S' is the surface
area and 'V' is the volume of a sphere, then
(i) S = 4πr2
(ii) V = (4/3)πr3
(5) Cylinder :
If 'r' is the radius (of
cross-section), 'h' is the height, 'L' is the lateral surface area, 'S' is the total surface
area and 'V' is the volume of a (right-circular) cylinder, then
(i) L = 2πrh
(ii) S = 2πrh + 2πr2 = 2πr(h + r)
(iii) V = πr2h
(6) Cone :
If 'r' is the base radius, 'h' is the
height, 'l' is the slant height, 'θ' is the semi-vertical angle, 'α' is
the vertical angle, 'L' is the lateral surface area, 'S' is the total surface area and 'V'
is the volume of a (right-circular) cone, then
(i) l2 = r2 + h2
(ii) tan θ = (r/h)
(iii) α = 2θ
(iv) L = πrl = πr√(r2 + h2)
(v) S = πrl + πr2 = πr√(r2 + h2) +
πr2
(vi) V = πr2h
(7) Simple pendulum :
If 'l ' is the length,
'T' is the period of oscillations of a simple pendulum and 'g' is the acceleration due to
gravity, then