**Volume of cube cuboid cylinder :**

Here we are going to see the formulas to be used to find volume of cube cuboid and cylinder.

Volume of cube = a^{3}

a = side length of cube

Volume of cuboid = l w h

l - length, w - width and h - height

Volume of cylinder = π r^{2} h

r - radius and h - height

**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 m^{3} ?

**Solution :**

Volume of one box = 0.8 m^{3}

Volume of godown = 60 **⋅** 40 ⋅ 30 = 72000 m^{3}

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 r^{2} h

= (22/7) ⋅ (7/4) ⋅ (7/4) ⋅ 4

= 38.5 cm^{3}

Hence the volume of the cylinder is 38.5 cm^{3}.

**Example 3 :**

Find the height of cuboid whose base area is 180 cm^{2} and volume is 900 cm^{3 }?

**Solution :**

The base of cuboid would be rectangle.

Base area of cuboid = 180 cm^{2}

length ⋅ width = 180

Volume of cuboid = 900 cm^{3}

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 m^{3} and diameter of the base is 140 cm ?

**Solution :**

Volume of cylinder = 1.54 m^{3}

diameter of base = 140 cm

radius = 140/2 = 70 cm

= 70/100 m = 0.7 m

Π r^{2} 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 r^{2} h

= (22/7) ⋅ (1.5)^{2 }⋅ 7

= 22 ⋅ (1.5)^{2}

= 49.5 m^{2}

1 m^{2} = 1000 liter

= 49.5 (1000)

= 49500 liter

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

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