Volume of a Sphere Calculator | Free Online Volume of a Sphere Calculator with Steps - BYJUS

# Volume of a Sphere Calculator

Volume of a sphere calculator is a free online tool that helps us calculate the volume of a sphere when the radius is known or the radius of the sphere when the volume is known. Let us familiarize ourselves with the calculator....Read MoreRead Less

## Online Volume of a Sphere Calculator

### How to use the ‘volume of a sphere calculator’?

Follow the steps below to use the volume of a sphere calculator:

1.
Enter the known measure (i.e., either the radius or the volume) into the respective input box and the unknown measure will be calculated. That is,

If you enter the radius as input, then the volume of the sphere will be calculated.

If you enter the volume as input, then the radius of the sphere will be calculated.

2.
Select the appropriate units for the input and output. .
3.
You can also select the desired value of ‘pi’ from the dropdown box. The values can be he following: 3.14, or $$\frac{22}{7}$$.
4.
To understand how we got that answer, click on the “Show steps”.
5.
On clicking the ‘Show steps’ button you will get the stepwise solution to find the missing measure.
6.
Click on the button to enter new inputs and start again.
7.
Click on the ‘Example’ button to play with different random input values.
8.
When you click on the ‘Explore’ button you can see how the volume of the sphere, cylinder and cone of the same radius and height (here taken as double of the radius) are related.
9.
When on the ‘Explore’ page, click the ‘Calculate’ button if you want to go back to the calculator.

### What is the Volume of a Sphere ?

The volume of a sphere refers to the amount of space the sphere occupies. A sphere is a three-dimensional round solid figure in which all points on its surface are at a fixed distance from a fixed point. The fixed distance is known as the radius of the sphere and the fixed point is known as the center of the sphere.

### Formulas used for the ‘volume of a sphere calculator’:

The volume of a sphere or the space occupied by it can be calculated using a standard formula. It is written as: When the radius is known the volume of a sphere can be written as:

Volume of a sphere, $$V=\frac{4}{3}\pi r^{3}$$

Where “r” represents the radius of the sphere.

When the volume of the sphere is known, the radius of the sphere can be written as:

Radius of a sphere, $$r=\sqrt{\frac{3V}{4\pi}}$$ ; where ‘V’ is the volume of the sphere.

### Relation between the volumes of spheres, cylinders and cones

Consider a sphere of radius r. The radii of the cylinder and cone are also r and their height is h, which is taken as 2r.

Volume of Sphere, $$V_{\text{sphere}}=\frac{4}{3}\pi r^3$$ Volume of Cylinder, $$V_{\text{cylinder}}=\pi r^2h$$ $$=\pi r^2\times 2r$$

$$=2\pi r^3$$

Volume of Cone, $$V_{\text{cone}}=\frac{1}{3}\pi r^2h$$ $$=\frac{1}{3}\pi r^2\times 2r$$

$$=\frac{2}{3}\pi r^3$$

Therefore,

$$V_{\text{sphere}}:V_{\text{cylinder}}:V_{\text{cone}}=\frac{4}{3}\pi r^3:2\pi r^3:\frac{2}{3}\pi r^3$$

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=4:6:2$$

On dividing by 2,

$$V_{\text{sphere}}:V_{\text{cylinder}}:V_{\text{cone}}=2:3:1$$

Hence the volume of the sphere is twice the volume of the cone and the volume of the cylinder is thrice the volume of the cone.

### Solved Examples on Volume of Sphere Calculator

Example 1:  Find the volume of a sphere whose diameter is 12 cm. (Take $$\pi=\frac{22}{7}$$).

Solution:

Given, diameter = 12 cm

So, radius = $$\frac{diameter}{2} = \frac{12}{2} = 6 ~ cm$$

$$\text{Volume}=\frac{4}{3}\pi r^{3}$$

$$V=\frac{4}{3} \times \pi \times 6^{3}$$

$$V=\frac{4}{3}\times\frac{22}{7}\times6^{3}$$

$$V=\frac{4}{3}\times\frac{22}{7}\times216$$

$$V=905.143~cm^3$$

Therefore, the volume of the sphere is 905.14 cubic centimeters.

Example 2: A sphere has a volume of $$14,130~ft^3$$. Find its radius. (Take $$\pi=3.14$$)

Solution: Given,

Volume of sphere, $$V = 14130$$ cubic feet

$$V=\frac{4}{3}\pi r^{3}$$

Therefore, $$r=\sqrt{\frac{3V}{4\pi}}$$

$$~~~~~~~~~~~~~~~~~~r=\sqrt{\frac{3\times 14130}{4\times 3.14}}$$

$$~~~~~~~~~~~~~~~~~~r=15$$ feet.

Therefore, the radius of the sphere is 15 feet.

### Any given sphere’s surface area (A) is equal to $$A=4\pi r^2$$; where the radius is denoted as ‘r.’

Consider a sphere with radius r: the surface area of the sphere is $$4\pi r^2$$ and its volume is $$\frac{4}{3}\pi r^3$$.

$$\Rightarrow \frac{\text{Volume of sphere}}{\text{Surface area of sphere}}=\frac{\frac{4}{3}\pi r^3}{4\pi r^2}=\frac{r}{3}=r:3$$

Let the initial volume of the sphere of radius $$r$$ be $$V$$ and the final volume of the sphere after doubling the radius be $$V_1$$. The radius now becomes $$r_1=2\times r$$;

$$\Rightarrow \frac{V_1}{V}=\frac{\frac{4}{3}\pi r_{1}^{3}}{\frac{4}{3}\pi r^3}=\left ( \frac{r_1}{r} \right )^3=\left ( \frac{2r}{r} \right )^3=\frac{2^3}{1}=\frac{8}{1}$$

Therefore, the volume of the sphere becomes eight times its initial volume, when the radius is doubled.

A sphere has only one surface.

Though both figures are round, a circle is a two-dimensional (2D) figure, whereas a sphere is a three-dimensional (3D) figure. Hence, the volume of a sphere can be calculated and not of a circle.