Cylinder Volume Formula and Area Of Square Formula

Cylinder Volume Formula

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= πr2h

Where,

V	Volume of cylinder
π	Value of 227
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 =πr2

Thus the volume of the cylinder will be,

V = Base area X-height

i.e. V = πr2Xh

i.e. V= πr2h

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= πr2h

i.e. V= πr2h

i.e. V= π×22×5

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 = πr2h

i.e. h = Vπr2

i.e. h = 1540227X7X7

i.e. h = 1540154

i.e. h =10 cm

Thus height of the cylinder will be 10 cm.

Area of Square Formula

When we talk about some plane figures, we think of their shape, region or boundary. We compare the objects based on their size and area. We all know that we need some measure to compare them. And one such measure is its area. All the objects that lie in a plane acquire some region of a flat surface. The measure of the surface enclosed by a closed figure is called its area. There are different geometrical closed shapes that exist namely square, rectangle, triangle, circle, etc. In this article, we will mainly be focusing on the understanding of the area of a square with some practical examples, its calculation, units. We will also focus on understanding the area of square formula. Let us start!

Area of Square Formula

What is Square?

Let us first understand the shape and structure of a square. A square is a four-sided rectangular closed figure on a plane. All the sides of a square have equal length. An object to be defined in two-dimensional geometry must have measured for length and breadth. Here, in the case of a square, its length and breadth are equal.

Let us consider the example of Ayesha. Ayesha makes pictures. She has made a collage on a square board with each side measuring 20 cm. She wants to laminate the collage and hence, wants to find the area of the square. To calculate the area of the college, she needs to multiply the measure of the length and breadth. Therefore, the area of the collage picture is the product of the sides of the collage.

Source: en.wikipedia.org

Hence, the area of a square is the product of the two sides of the square. It is also known as squares of the sides. As the area of a square is a product of the two sides, the unit of the area is in square units. In the above example, the area of the collage comes out to be 40 and the unit of area is square centimeter. Hence, the total area of the collage is 40 square centimeters.

Square Formula

Area =a²

Where,

A	Area of Square
a	Side of the square

Area of Square Formula Derivation

To better our understanding of the concept, let us take a look at the derivation of the area of Square formula. Let us consider a square as a rectangular object whose length is of a unit and breadth is of a unit. As we know the area of the rectangle is given by,

A =  L × B

Where

A	Area of the square
l	Length of the rectangular object
b	The breadth of a rectangular object

A = l × b

A = a × b

= a × a = a² = a²

Solved Examples on Area of Square Formula

Now that we have some clarity about the concept and meaning of the area of the square, let us try some examples to deepen our understanding of the subject.

Q: Find the area of a square plot of side 8 m.

Ans: As we already have a formula for calculating the area of a square. Let us substitute the values

A = a × a = a² = a²

A = 8²

= 64 sq m

Q: A square of 10 cm long is cut into tiny squares of 2 cm long. Calculate the number of tiny squares that can be created.

Ans: Since the length of the big square is 10 cm, hence its Area A is:,

A= a × a = a² = a²

A = 10² = 100 cm²

Now, since the length of tiny square is 2 cm, hence its Area is:

A =  a × b

= 2 × 2

= 2 × 2 = 2²

= 4 sq cm.

Therefore, the number of squares that we can create are:

Number of Squares = AreaofBigSqaureAreaofTinySquares

= 1004

Number of Squares = 25