Height Of A Cylinder Equation

The volume of a cylinder is the density of the cylinder which signifies the amount of cloth it can carry or how much amount of any material can be immersed in it. Cylinder's volume is given by the formula,πr²h, where r is the radius of the circular base and h is the meridian of the cylinder. The material could exist a liquid quantity or any substance which can be filled in the cylinder uniformly. Check volume of shapes here.

Volume of cylinder has been explained in this commodity briefly forth with solved examples for amend understanding. In Mathematics, geometry is an important co-operative where we learn the shapes and their backdrop. Volume and surface area are the two important backdrop of any 3d shape.

Also read:

Volume of A Cylinder Calculator
Volume Of A Cylinder Formula
Volume Of Cone
Surface Area Of A Cylinder
Important Questions Class 9 Maths Chapter thirteen Surface Areas Volumes
Of import Questions Form 10 Maths Chapter 13 Surface Areas Book

Definition

The cylinder is a three-dimensional shape having a circular base. A cylinder can be seen every bit a fix of circular disks that are stacked on one some other. Now, retrieve of a scenario where we demand to summate the corporeality of sugar that can be accommodated in a cylindrical box.

In other words, we hateful to calculate the capacity or volume of this box. The capacity of a cylindrical box is basically equal to the volume of the cylinder involved. Thus, the volume of a three-dimensional shape is equal to the amount of space occupied by that shape.

Volume of a Cylinder Formula

A cylinder can be seen equally a collection of multiple congruent disks, stacked one above the other. In order to summate the space occupied by a cylinder, we summate the space occupied past each disk so add them upwards. Thus, the book of the cylinder can exist given past the product of the area of base and height.

Volume of a Cylinder

For any cylinder with base of operations radius 'r', and pinnacle 'h', the volume will be base times the height.

Therefore, the cylinder's volume of base radius 'r', and height 'h' = (surface area of base) × height of the cylinder

Since the base is the circumvolve, it can be written every bit

Volume = πr²× h

Therefore, the volume of a cylinder = πr²h cubic units.

Book of Hollow Cylinder

In example of hollow cylinder, we measure out 2 radius, i for inner circumvolve and one for outer circumvolve formed past the base of hollow cylinder. Suppose, r₁ and r₂ are the 2 radii of the given hollow cylinder with 'h' as the elevation, then the volume of this cylinder can be written every bit;

Five = πh(r_i ² – r₂ ^two)

Expanse of Cylinder

The amount of square units required to cover the surface of the cylinder is the surface expanse of the cylinder. The formula for the expanse of the cylinder is equal to the full surface area of the bases of the cylinder and surface area of its sides.

A = 2πr² + 2πrh

Volume of Cylinder in Litres

When we notice the volume of the cylinder in cubic centimetres, we tin can catechumen the value in litres by knowing the below conversion, i.e.,

one Litre = 1000 cubic cm or cm³
For example: If a cylindrical tube has a volume of 12 litres, then we can write the volume of the tube as 12 × 1000 cm^three = 12,000 cm³

Examples

Question 1: Calculate the volume of a given cylinder having acme 20 cm and base radius of 14 cm. (Take pi = 22/seven)

Solution:

Given:

Height = 20 cm

radius = 14 cm

nosotros know that;

Book, 5 = πr^twoh cubic units

V=(22/7) × fourteen × xiv × xx

V= 12320 cm³

Therefore, the volume of a cylinder = 12320 cm^three

Question two: Calculate the radius of the base of a cylindrical container of volume 440 cm³. Height of the cylindrical container is 35 cm. (Take pi = 22/7)

Solution:

Given:

Book = 440 cm³

Height = 35 cm

We know from the formula of cylinder;

Volume, V = πr^twoh cubic units

So, 440 =(22/7) × r² × 35

r²= (440× 7)/(22 × 35) = 3080/770 = four

Therefore, r = two cm

Therefore, the radius of a cylinder = 2 cm.

Frequently Asked Questions on Volume of a Cylinder

What is meant by the volume of a cylinder?

In geometry, the volume of a cylinder is defined every bit the capacity of the cylinder, which helps to discover the amount of material that the cylinder tin agree.

What is the formula for the volume of a cylinder?

The formula to calculate volume of a cylinder is given by the product of base of operations area and its height.
Since, the base expanse of a cylinder is circular, we tin state that
Volume of a cylinder = πr^twoh cubic units.

What is the volume of a hollow cylinder?

As we know, the hollow cylinder is a type of cylinder, which is empty from inside and it should possess some divergence between the internal and the external radius. Thus, the amount of infinite occupied by the hollow cylinder in the iii dimensional space is chosen the book of a hollow cylinder.

How to summate the volume of a hollow cylinder?

If R is the external radius and r is the internal radius, then the formula for computing the cylinder's book is given past:
V = π (R² – r²) h cubic units.

What is the unit for the book of a cylinder?

The volume of a cylinder is generally measured in cubic units, such as cubic centimeters (cm³), cubic meters (grand³), cubic feet (ft³) and so on.

How to find the volume of a cylinder if the diameter and meridian are given?

Equally we know, Diameter "d" = 2(Radius) = 2r.
So, r = d/two
At present, substitute the value of "r" in the volume of cylinder formula, we become
V = πr^twoh = π(d/2)²h
V = (πd²h)/iv
Hence, the volume of the cylinder is (πd²h)/four, if its diameter and height are given.

What will happen to the cylinder's volume if its radius is doubled?

As we know, cylinder's volume is direct proportional to the square of its radius.
If the radius is doubled, (i.e., r = 2r), we get
Five = πr²h =π(2r)^twoh = 4πr²h.
Hence, the cylinder'southward volume becomes four times, when its radius is doubled.

What volition happen to the cylinder's volume if its radius is halved?

We know that, the volume of cylinder ∝ Radius2
Thus, if radius is halved, (i.due east., r = r/2), nosotros get
V = π(r/two)²h = (πr^twoh)/iv
Therefore, the cylinder'southward book becomes ane/quaternary, if its radius is halved.