Aptitude Round Question-Volume & Surface of Areas-Free Download

Formula for geometrical figures

pi (p)=3.1415926535 ...

Perimeter formula
Square	4 � side
Rectangle	2 � (length + width)
Parallelogram	2 � (side1 + side2)
Triangle	side1 + side2 + side3
Regular n-polygon	n � side
Trapezoid	height � (base1 + base2) / 2
Trapezoid	base1 + base2 + height � [csc(theta1) + csc(theta2)]
Circle	2 � pi � radius
Ellipse	4 � radius1 � E(k,pi/2) E(k,pi/2) is the Complete Elliptic Integral of the Second Kind k = (1/radius1) � sqrt(radius1² - radius2 ²)
Area formula
Square	side²
Rectangle	length � width
Parallelogram	base � height
Triangle	base � height / 2
Regular n-polygon	(1/4) � n � side² � cot(pi/n)
Trapezoid	height � (base1 + base2) / 2
Circle	pi � radius²
Ellipse	pi � radius1 � radius2
Cube (surface)	6 � side²
Sphere (surface)	4 � pi � radius²
Cylinder (surface of side)	perimeter of circle � height
	2 � pi � radius � height
Cylinder (whole surface)	Areas of top and bottom circles + Area of the side
	2(pi � radius²) + 2 � pi � radius � height
Cone (surface)	pi � radius � side
Torus (surface)	pi² � (radius2² - radius1² )
Volume formula
Cube	side³
Rectangular Prism	side1 � side2 � side3
Sphere	(4/3) � pi � radius³
Ellipsoid	(4/3) � pi � radius1 � radius2 � radius3
Cylinder	pi � radius² � height
Cone	(1/3) � pi � radius² � height
Pyramid	(1/3) � (base area) � height
Torus	(1/4) � pi² � (r1 + r2) � (r1 - r2)²

If l, b and h are length, breadth and height of a cuboid, then
� lateral surface area = 2h (l + b)
� total surface area of the cuboid = 2(lb + bh + lh)
� volume = lbh

If 'a' is the length of the edge of a cube, then
� lateral surface area of the cube = 4a²
� total surface area of the cube = 6a²
� volume = a³

Curved surface area of a cylinder (CSA) = 2prh.

Total surface area of a cylinder (TSA) = 2prh + 2pr² = 2pr(h + r).

Volume of a cylinder (V) = pr²h.

Base area of the cone = pr²

Curved surface area of the cone = prl

Total surface area of the cone = prl + pr² = pr(l + r)

Volume of the cone = 1 3 pr²h

Surface area of a sphere (A) = 4pr²

Volume of a sphere (V) = 4 3 pr³

Surface area of a hemisphere = 2pr²

Total surface area of a hemisphere = 3pr²

Volume of a hemisphere = 2 3 pr³

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