Volume & Surface Area

 

Cuboid

 
1. Volume of Cuboid = Length X Breadth X Height = l X b X h
2. Surface Area of Cuboid = 2(lb+bh+lh)
3. Diagonal of Cuboid 
 

Cube

 
1. Volume of Cube = a3
2. Surface Area of Cube = Area of 6 Sides = 6a2
3. Diagonal of Cube
 
 

Cylinder

1. Volume of Cylinder = πr2h
2. Curved Surface Area of Cylinder = 2πrh
3. Total Surface Area of Cylinder = Curved Surface Area + Area of 2 bases = 2πrh+2πr2 = 2πr(r+h)
 

Cone

 
1. Slant height of Cone
 
2. Volume of Cone
 
3. Surface Area of Cone
 
4. Total Surface Area of Cone
 

Sphere

 
1. Volume of Sphere 
2. Curved Surface Area of Sphere = 4πr2
 
where 'r' is the radius of Sphere 
 

Hemisphere

 
1. Volume of hemisphere
2. Curved Surface Area of hemisphere = 2πr2
3. Total Surface Area of hemisphere = 3πr2
 
where 'r' is the radius of hemisphere 
 

Hollow Sphere

1. Volume of Hollow Sphere
 

Prism 

 
1. Volume of Prism = Area of base X height
2. Lateral Surface Area of Prism = Perimeter of Base X height
3. Total Surface Area of Prism = Lateral Surface Area of Prism + (2 X Area of Base)
 
 

Pyramid

 
1. Volume of Pyramid = 1/3 X area of base X height
2. Total Surface Area of Pyramid = Area of Base + Lateral Area
 

Note:

1. Three cubes of metals of side a, b and c respectively, recast into a cube. If there is no loss of weight during this process. Then side of new cube will be=
 
2.  If a cube of side a recast into the small cubes of side b, then the number of small cubes=
 
3. If a sphere of radius r recast into cylinder of radius b, then the height of cylinder=
 
4. If the length, breadth & height of cuboid are increased by x%, y% abd z% respectivley, then the volume of cuboid is increased by:
 
5. If each side of a cube is increased by x%, then the volume of cube is increased by: