Top

# Sphere

The sphere is a perfect three dimensional circular shape. It is symmetric around its center. The sphere is a closed surface. Like the circle in 2 dimensions, the spheres have all the points on it at the same distance from the center of the sphere. A sphere is formed by all the points in space which are at the same distance from a fixed point.

 Related Calculators Sphere Calculator Volume a Sphere Sphere Surface Area Calculator

## Sphere Definition

A sphere is a three dimensional circular object. It is the set of points which are equidistant from a fixed point. This distance between points and fixed point is known as the radius of the sphere, and the given point is known as the center of the sphere. If the set of points of distance one from the centre then the sphere is unit sphere.

## Sphere Formula

Let r be the radius of sphere
• Volume of sphere = $\frac{4}{3}$ $\pi$ $r^3$
• Surface area of sphere = 4 $\pi r^2$
• Diameter of sphere = Twice of radius = 2 $\times$ Radius

## Sphere Equation

The general equation of a sphere with center at $(x_0, y_0, z_0)$ and radius r is,

$(x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 = r^2$

The general equation of a sphere is used in calculating the center and radius of the sphere.

And equation of a sphere of radius r centered at the origin

Put $(x_0, y_0, z_0)$ $\rightarrow$ (0, 0, 0)

=> $x^2 + y^2 + z^2 = r^2$

## Volume of Sphere

Volume of a Sphere is a measurement of the occupied units of a Sphere

The formula for calculating the volume of a sphere with radius 'r' is given by,

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

## Surface Area Sphere

Surface Area of a Sphere is the measure of how much exposed area a sphere has.

The formula for calculating the area of a sphere with radius 'r' is given by,

Surface area = 4 $\pi r^2$

## Half Sphere

Half of a sphere is also called as hemisphere. A sphere is divided into two equal halves when a plane passing through its center. Half sphere has one flat surface, one curved and one edge.

## Sphere Shaped Objects

Below you could see some objects are in the shape of a sphere -

## Calculate Sphere

Given below are some of the examples on sphere.

### Solved Examples

Question 1: Calculate the surface area and the volume of the sphere with radius 4 cm.
Solution:

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

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

= $\frac{4}{3}$ $\times \pi \times 64$

= 268

Volume of a sphere is 268 cm$^3$

Surface area of a sphere = $4 \times \pi \times r^2$

= $4 \times \pi \times 4^2$

= $4 \times \pi \times 16$

= 201 cm2

Surface area of sphere is 201 cm2

Question 2: Calculate the surface area and the volume of the sphere with radius 5.5 cm.
Solution:

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

= $\frac{4}{3}$ $\times \pi \times (5.5) ^3$

= $\frac{4}{3}$ $\times \pi \times 166.37$

= 696.9

Volume of sphere is 696.9 cm $^3$

Surface area of a sphere = $4 \times \pi \times r^2$

= $4 \times \pi \times (5.5)^2$

= $4 \times \pi \times 30.25$

= 380.1

Surface area of sphere is 380.1 cm2

Question 3: Find the volume of a solid spherical object, whose radius is 6 centimeter.
Solution:

The volume of sphere = $\frac{4}{3}$ $\pi r^3$ cubic units

= $\frac{4}{3}$ $\times 3.14 \times 6 \times 6 \times 6$

= 904.32 cubic centimeter.

So, the volume of the given sphere is 904.32 cubic centimeter.