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.

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Sphere Calculator | Volume a Sphere |

Sphere Surface Area Calculator | |

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 Shape:

Let r be the radius of sphere

Below you could see some objects are in the shape of a 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: **

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

** Solution: **

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

** Solution: **

Given below are some of the practice problems on sphere. ### Practice Problems

**Question 1: **Calculate the surface area and the volume of the sphere with radius 3.2 cm.

**Question 2: **Calculate the surface area and the volume of the sphere with radius 4.1 cm.

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

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 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 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 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.

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

Given below are some of the examples on sphere.

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 cm^{2}

Surface area of sphere is 201 cm^{2}

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 cm^{2}

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.

More topics in Sphere | |

Surface Area of a Sphere | Volume of a Sphere |

Great Circle | Antipodal Point |

Spheroid | Partial Sums |

Properties of Sphere | Difference between Circle and Sphere |

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