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Formula for Surface Area and Volume

Surface Area and Volume Formula:

The surface area of a solid  geometric figure is the sum of the area of all surfaces of a figure. Volume of the figure gives the quantity of space occupied.

Surface area and volume formula of the geometric figure are given below

 Sl.No   Figure   Formula for surface area  Formula for volume
 1  Rectangular Prism

Rectangular Prism
 SA = 2ab+2bc+2ca  sq. units
 where a, b,c are the sides of the cube.
 V = abc  cubic units 
 2  Cylinder 

Cylinder Diagram
  SA = 2πrh  sq. units
  TSA =  2πr(h+r)  sq. units 
  r =radius of the cylinder
  h – height of the cylinder
 V = πr2h   cubic units
 3  Cube 

Cube Unit
  SA = 6a2  sq. units 
  a = sides of the cube
  V = a3    cubic units 
 4   Sphere

The Sphere
  SA = 4πr2    sq. units
  r = radius of the sphere
 V = $\frac{4}{3}$ πr3   cubic units 
 5   Ellipsoid

  SA = $4\pi \left [ \frac{a^pb^p+a^pc^p+b^pc^p}{3} \right ]^{\frac{1}{p}}$
 p = 1.6075
 a, b, c are semi axis of ellipsoid 
 V = $\frac{4}{3}$ π r1,r2,r3  cubic units
 6   Cone 

Cone Diagram
 CSA = πrl sq. units   V = $\frac{1}{3}$ πr2h   cubic units
 7   Pyramid 

Perimeter of Pyramid
   SA = a + $\frac{1}{2}$ *p*l
   p = perimeter of pyramid
   l = slant height
   a= area of the base of the pyramid
 V = $\frac{1}{3}$ *a*h  cubic units 
 8   Torus

  SA =  π2 * (R2 - r2
  R: Outer Radius
  r: Inner Radius 
 V = $\frac{1}{4}$ π3 (r+ r2) (r- r2)2  cubic units 
 9   Hemisphere

Hemisphere Radus
  CSA = 2πr2 
  TSA = 3πr2
  r = radius
 V = $\frac{2}{3}$ πr3   cubic units 
 10  Triangle 

Triangle Picture
 SA = $\sqrt{s(s-a)(s-b)(s-c)}$
 where s is the perimeter of the triangle
 a, b, c are the sides of the triangle 
 11  Rectangle 

Rectangle Width
 A = l*w

 L = length
 w = width 
 12  Triangle 

Triangle Figure
 A = $\frac{1}{2}$ bh
 b = base  h = height 
 13  Trapezoid  

Trapezoid Diagram
  A = $\frac{1}{2}$ h (b1+b2)   
 14  Parallelogram

  A = bh   
 15  Circle 

Circle Radius
  A = πr2   r = radius