Rectangle Formula and Volume Of Sphere Formula

Rectangle Formula

We may have come across many objects in our daily life which is rectangular in shape. Some objects of this type of shape are playground, an A4 sheet of paper, room wall, etc. In this article, we will discuss rectangles, some related terms and definitions and also rectangle formula with examples. Let’s start learning!

Rectangle Formula

What is a Rectangle?

There are many authentic and real-life purposes where we would need to calculate some measurements of various shapes. For example, suppose we are looking to sod our lawn, then we would need to know the area of our lawn in order to implant grass in it. Or, we may wish to do fencing of the playground in a rectangular shape.

Thus rectangle is a very common shape in our daily life. A rectangle is any four-sided figure with four right angles i.e. 90-degree angles and with equal length of opposite sides. If we look around us, then we can see many examples. Most likely, the room in which we are sitting in some form of a rectangle or a combination of rectangles.

To recall, a rectangle is a four-sided polygon and the length of the opposite sides is equal. A rectangle is also called an equiangular quadrilateral, as all the angles of a rectangle are right-angled. A rectangle is a parallelogram with right angles in it.

When the four sides of a rectangle are made equal, then it is called a square. We have to perform a various measurements to complete some important tasks. Some measurement in rectangle as Perimeter, Diagonal, Area, etc. of the rectangle

Some terms related to this shape are as follows:

1. Length: It is the longer side of the rectangle.
2. Breadth: It is the smaller side of the rectangle.
3. Diagonal: It is the direct straight line distance between two opposite vertices of the rectangle.
4. Perimeter: It is the sum total of all four sides of the rectangle.
5. Area: Area of the rectangle describes the amount of space covered by it. So, it will give the coverage of the rectangle as a two-dimensional plane.

Some important Rectangle Formula:

1. The perimeter of the rectangle:

P= 2 × (l+ b)

Where,

P	Perimeter
l	Length
b	Breadth

2. Diagonal of the rectangle:

D= (l2+b2)12

Where,

D	Diagonal
L	Length
b	Breadth

3. Area of the rectangle:

A= l × b

A	Area
L	Length
b	Breadth

Solved Examples

Q. Find out the length of the rectangle if its area is 96 cm2 and the breadth is 16 cm.

Solution:

As we know,

Area of a rectangle = l × b

Here the area is already given in the question. So,

A= l × b

B=al

B=9616

B = 6 cm

Q. Find the perimeter of a rectangle whose length and width is 20 cm and 9 cm respectively.

Solution:

Here given values in the question are,

l = 20 cm

b = 9 cm

Perimeter of Rectangle,

P = 2 × (l + b)

= 2 × (20 +9) cm

= 2 × 29 cm

Hence, the perimeter of a rectangle = 58 cm

Volume of Sphere Formula

Take a ball, for example. A ball is an object in the shape of a sphere. But are we knowing about its definition? If we take a close look, then we will see that it has no corners or edges. Also, it does not matter how we hold the ball. Its each one of the points will be the same distance to the very center of the ball. Spheres are three-dimensional shapes. We can see spheres every day in our surroundings. This article will see its definition, some related terms and the volume of sphere formula of various measurements. Let us learn about this very common shape.

Volume of a Sphere Formula

What is the Sphere?

Is it the same as a circle? The answer is No. Because we can draw a circle on a paper, but we cannot draw the sphere on a paper. This is because circle is a two-dimensional object and sphere is a three-dimensional object.

If we paste a string along the diameter of a circular disc and rotate it then we will see a new solid shape, which is a sphere. So, a sphere is a three-dimensional figure, which is made up of all points in the space. These points lie at a constant distance called the radius, from a fixed point called the center of the sphere.

Volume of a Sphere:

In our everyday life, we come across different types of spheres like Basketball, football, table tennis, etc. The balls used in these sports are nothing but spheres, of course with different radii. The volume of sphere formula is useful for designing and calculating the capacity or volume of such spherical objects. We can easily find out the volume of a sphere if we know its radius.

The volume of the sphere will also represent the capacity to store some material within this type of object. Thus, the volume is also defined as the capacity of a three-dimensional object. Therefore the volume of a sphere is nothing but the space occupied by it. It can be computed as:

V= 43×Π×R3

V	Volume
R	The radius of the sphere

Solved Examples

Q. A spherical shaped tank has a radius of 21 m. Find the capacity of it in liter to store water in it.

Solution: In this question it is given,

R = 21 m

We know that, volume of a sphere,

V= 43×Π×R3

V = 43×227×21×21×21

V = 4 × 22 × 21 × 21

V= 38808 cubic m

Also we know that,

1 cubic m = 1000 liter

Thus capacity of tank,

= 38808 cubic m × 1000

= 38808000 liter.

Thus 38808000 Liter water can be stored in the tank.

Q. The volume of a spherical ball is 343 cm3. What will be the radius of the ball?

Solution: In the question it is given,

Volume of the sphere= 343 cm3

We know that, volume of a sphere,

V= 43×Π×R3

i.e. R3=34×VΠ

R = (34×V3.14)13

= (34×3433.14)13

= 81.92 cm

= 4.34 cm

Thus radius is 4.34 cm.