VOLUME OF CUBE CUBOID CYLINDER

Cube 

Volume of cube  =  a³

a = side length of cube

Cuboid 

Volume of cuboid  = l w h

l - length, w - width and h - height

Cylinder

Volume of cylinder  =   π r² h

r - radius and h - height

Solved Examples

Example 1 :

A godown is in the form of cuboid of measures 60 m x 40 m x 30 m. How many cuboidal boxes can be stored in it if the volume of one box is 0.8 m³ ?

Solution :

Volume of one box  =  0.8 m³

Volume of godown  =  60 ⋅ 40 ⋅ 30  =  72000 m³

Number of boxes that can be stored in the godown  =  Volume of godown / Volume of one box

  =  (60 ⋅ 40 ⋅ 30) / (0.8)

  =  90000

Hence the number of cuboidal boxes that can be stores in the godown is 90000.

Example 2 :

A rectangular piece of paper 11 cm x 4 cm is folded without overlapping to make a cylinder of height 4 cm. Find the volume of cylinder.

Solution :

Length of paper becomes the perimeter of the base of the cylinder and width becomes height.

Let radius of the cylinder  =  r and height  =  h

Perimeter of base of the cylinder  =  2 Π r  =  11

2 ⋅ (22/7) ⋅ r  =  11

r  =  11 ⋅ (7/22) ⋅ (1/2)

r  =  7/4 cm

Volume of cylinder  =  Π r² h

  =  (22/7)  ⋅ (7/4) ⋅ (7/4) ⋅  4

  =  38.5 cm³

Hence the volume of the cylinder is 38.5 cm³.

Example 3 :

Find the height of cuboid whose base area is 180 cm² and volume is 900 cm³ ?

Solution :

The base of cuboid would be rectangle.

Base area of cuboid  =  180 cm²

length ⋅ width  =  180

Volume of cuboid  =  900 cm³

length ⋅ width ⋅ height  =  900

180 ⋅ height  =  900

height  =  900 / 180

  =  5 cm

Hence the height of cuboid is 5 cm.

Example 4 :

Find the height of the cylinder whose volume is 1.54 m³ and diameter of the base is 140 cm ?

Solution :

Volume of cylinder  =  1.54 m³

diameter of base  =  140 cm

radius  =  140/2  =  70 cm

  =  70/100 m  = 0.7 m 

 Π r² h  =  1.54

(22/7)  ⋅ 0.7 ⋅ 0.7 ⋅  h  =  1.54

22 ⋅ 0.1 ⋅ 0.7 ⋅ h  =  1.54

h  =  1.54/(22 ⋅ 0.1 ⋅ 0.7)

h  =  1.54/1.54

h  =  1 m

Hence height of cylinder is 1 m

Example 5 :

A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in liters that can be stored in the tank ?

Solution :

Radius of milk tank (r)  =  1.5 m

Length of milk tank (h)  =  7 m

To find the quantity of milk stored in the tank, we have to find the volume of cylindrical tank.

Volume of cylinder  =   Π r² h  

  =  (22/7) ⋅ (1.5)² ⋅ 7

  =  22 ⋅ (1.5)²

  =  49.5 m²

1 m²  =  1000 liter

  =  49.5 (1000) 

  =  49500 liter

Hence the quantity of milk stored in the tank is 49500 liter.

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