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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= \(\frac{4}{3} × \Pi × R^3\)

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= \(\frac{4}{3}× \Pi × R^3\)

V = \(\frac{4}{3} ×  \frac{22}{7} × 21 × 21× 21\)

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= \(\frac{4}{3} × \Pi × R^3\)

i.e. \(R^3 = \frac{3}{4} × \frac{V}{\Pi }\)

R = \((\frac{3}{4} × \frac{V}{3.14})^\frac{1}{3}\)

= \((\frac{3}{4}× \frac{343}{3.14})^\frac{1}{3}\)

= 81.92 cm

= 4.34 cm

Thus radius is 4.34 cm.

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