In our day to day life, we have seen many objects in a very common shape i.e. cylinder. Some examples are a bottle, drum, gas container, water pipes, etc. A cylinder is a closed shape that has two parallel usually circular bases that are connected by a curved surface. If we take it apart then we will find it has two ends, called bases, generally circular. In this topic, the student will learn about the shape of a cylinder with the cylinder volume formula and its examples. Let us begin it!

**Cylinder Volume Formula**

**What is the cylinder?**

A cylinder is a three-dimensional shape of solid objects with two round flat bases and one curved side. It has a curved surface in the middle of its two bases. The base and the top surface are identical. And usually as a circular plane. Thus the bases are always parallel and congruent to each other. Note that the cylinder has no vertex.

When the two bases are exactly over each other and the axis of the cylinder is at a right angle to its circular base, then this type of cylinder is called a ‘right circular cylinder’.

If one base is displaced along aside, then the axis will not be at right angles to its circular base and hence the resultant shape will be known as an oblique cylinder. The bases in oblique cylinder although not directly over each other, but are still parallel.

**How to compute the volume of a cylinder?**

The formula for the volume of a cylinder is given as:

**V= \( \pi r^2 h \)**

Where,

V | Volume of cylinder |

\( \pi \) | Value of \( \frac{22}{7} \) |

r | The radius of the circular base |

h | Height of cylinder |

** ****Derivation**

Although a cylinder is technically not as a prism, it shares many properties of a prism. For example, like a prism, the volume of a cylinder can be found by multiplying the area of its circular base by its height.

Here the base of the cylinder is a circle.

Therefore, the area of this circular base is given by the formula:

A =\( \pi r^2 \)

Thus the volume of the cylinder will be,

V = Base area X-height

i.e. V = \( \pi r^2 X h \)

i.e. V= \( \pi r^2 h \)

Hence proved.

**Solved Examples**

Q. 1: Calculate the Volume of a right circular cylinder if the radius of its base is 2 cm and height is 5 cm.

Solution: As given in the question:

r = 2 cm

h = 5 cm

So, Volume of cylinder,

V= \( \pi r^2 h \)

i.e. V= \( \pi r^2 h \)

i.e. V= \( \pi × 2^2 × 5 \)

i.e. V = \( 3.14 × 4 × 5 \)

i.e. V = 62.8 cubic cm.

Thus the volume of the cylinder is 62.8 cubic cm.

Q. 2: Find the height of a cylinder with a circular base of radius 7 cm and volume 1540 cubic cm.

Solution: A given here,

r= 7 cm

V= 1540 cubic cm

And we have to compute the height of the cylinder.

Since,

V = \( \pi r^2 h \)

i.e. h = \( \frac{V}{\pi r^2} \)

i.e. h = \( \frac{1540}{\frac{22}{7} X 7 X 7} \)

i.e. h = \( \frac{1540}{154} \)

i.e. h =10 cm

Thus height of the cylinder will be 10 cm.

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