Vertical Volume Liquid – Definition With Examples

What Is Vertical Volume Liquid?

When Jo drank water from her water bottle on a sunny day, she got curious about something. Jo was curious about the amount of water her water bottle could carry.

As we know, water is shapeless. It takes the shape of the container you put it in. Therefore, if we can find the volume of Jo’s water bottle, we can figure out the volume of water in it. Vertical volume liquid is the volume of a given amount of liquid, i.e., the amount of space a liquid takes up in any container.

The Volume of Different Shapes

Volume is the product of the surface area of an object and its depth/height, provided it rises uniformly from the base. Look at the figure below:

A cylinder

In the picture above, we get a cylinder when a two-dimensional figure (circle) acquires a depth/ height and rises uniformly from the base. So, we can say that:

The formula for volume of liquid in a vertical cylinder = (area of a circle) πr² × h (height of the cylinder)

Similarly, we have standard formulas for finding the volume of each solid:

Formulas for volume of solid shapes

Solved Examples

Example 1: Find the volume of water that a cubical water tank of length 2 m can hold. 

Solution:

A cube with side length 2 m

The volume of water the given tank can hold = volume of a cube = $a^3$.

Length of each side of given tank = a = 2 m

So, the volume of water the tank can hold =  $a^3$ = 2 × 2 × 2 = 8 cubic meter.

Therefore, the volume of water the given cubical tank can hold is 8 cubic meters.

Example 2: An ice cream scoop over a cone melts completely so that the cone is filled with melted ice cream to the brim. Find the volume of the liquid ice cream in the cone if its height is 12 cm and the base radius is 3.5 cm.

Solution:

A cone with radius 3.5 cm and height 12 cm

The volume of liquid ice cream inside the ice cream cone = volume of a cone = $\frac{1}{3} πr²h$

Given,

The height of the ice cream cone = h = 12 cm

Base radius of the cone = r = 3.5 cm

Therefore, 

Volume of melted ice cream in the cone = $\frac{1}{3} πr²h$

                                                                = $\frac{1}{3}$ × 3.14 × 3.5 × 3.5 × 12 

                                                                 = 153.86 cubic cm.

Example 3: Find the volume of water that a cuboidal reservoir of length 4 m, width 2 m, and depth 1 m can hold.

Solution:

A cuboid with dimensions 2 m, 4 m, and 1 m

The volume of water a cuboidal reservoir can hold = volume of a cuboid = lbh

Given,

l = 4 m

b = 2 m

h = 1 m

Therefore, the volume of water the given reservoir can hold = 4 × 2 × 1 = 8 cubic meters.

Practice Problems

Vertical Volume Liquid - Definition With Examples

Attend this quiz & Test your knowledge.

1A cylindrical bottle has a base radius of 7 cm and a height of 10 cm. It has water up to the brim. Calculate liquid volume of the vertical cylinder.

1450.5 cubic cm
1538.6 cubic cm
1630.5 cubic cm
1360 cubic cm
CorrectIncorrect
Correct answer is: 1538.6 cubic cm
The volume of water inside the bottle = Volume of a cylinder $= πr²h$
Given,
$r = 7$ cm
$h = 10$ cm
Therefore,
Volume of the water inside the given bottle $= πr²h = 3.15 × 7 × 7 × 10 = 1538.6$ cubic cm

2The volume of water a spherical earthen pot of radius 3 cm can hold is (use $π = 3.14$):

117.63 cubic cm
113.04 cubic cm
125.08 cubic cm
100 cubic cm
CorrectIncorrect
Correct answer is: 117.63 cubic cm
The volume of water the given spherical pot can hold = volume of a sphere = $\frac{4}{3} πr^3$
For the given spherical earthen pot, r = 3 cm.
Therefore,
Volume of water the given sphere can hold = $\frac{4}{3} πr^3 = \frac{4}{3} \times 3.14 \times 3 \times 3 \times 3 = 36 \times 3.14$
= $113.04$ cubic cm.
Vertical Volume Liquid – Definition With Examples

3The volume of water a cubical tank of side 3 m can hold is

27 cubic meters
16 cubic meters
24 cubic meters
32 cubic meters
CorrectIncorrect
Correct answer is: 27 cubic meters
The volume of water the given tank can hold = volume of a cube = $a^3$
Length of each side of given tank $= a = 3$ m
So, the volume of water the tank can hold = $a^3$ $= 3 × 3 × 3 = 27$ cubic meter
Vertical Volume Liquid – Definition With Examples

Frequently Asked Questions

You can only apply the conventional formula when a solid evenly rises from the base. Cone does not satisfy this condition as it tapers towards the top.

The SI unit of volume in cubic meters.

“Litre” is a unit measuring the vertical volume of liquid, equal to 1000 cubic meters or one cubic decimeter.

No, two-dimensional shapes do not have volume.