# How To Find The Volume and Surface Area of Spheres

Updated: Nov 16, 2021

__In this note, you will learn:__

· __What are spheres?__

· __Volume and surface area of spheres__

· __Application questions involving volume and surface area of spheres__

__What is a sphere?__

__What is a sphere?__

Based on geometrical terms, A sphere is a three-dimensional geometrical object that is identical to a ball, and every point on its surface is ** equidistant** (having the same distance) from its center.

The main dimension to know about a sphere is very simple: its ** radius**. The radius of a sphere is measured from

**.**

__the center of the sphere to any point on the surface of the sphere__**How to find the volume of sphere?**

**How to find the volume of sphere?**

The general formula to find the volume of a sphere is:

**V = 4/3 **π r^3

where ** V** is the

**of the sphere and**

__volume__**is the**

__r__**of the sphere**

__radius__**How to find the surface area of spheres?**

**How to find the surface area of spheres?**

The general formula to find the total surface area of a sphere is:

**Total Area = 4 π r^2**

where ** r** is the

**of the sphere**

__radius____Application examples involving spheres__

__Application examples involving spheres__

__Finding the volume of a sphere__

A ball bearing (which is spherical in shape) has a radius of 2.4 cm. Find

i) the volume of the ball bearing,

ii) the mass of 2500 identical ball bearings if they are made of wood of density 1.5 g/cm^3.

Solution:

i) Volume of ball bearing = **4/3 π r^3 **

= 4/3 x π x (2.4)^3

= 1.8432π cm^3

= 57.9 cm^3 (to 3 s.f.)

ii) Mass of 2500 ball bearings = volume of 2500 ball bearings × density

= 2500 × 18.432π × 1.5

= 217 000 g (to 3 s.f.)

__Finding the total surface area of a sphere__

A solid sphere has a diameter of 7.8 cm. Find its surface area.

Solution:

Radius of sphere = 7.8 ÷ 2

= 3.9 cm

Surface area of sphere = 4πr^2

= 4 × π × (3.9)^2

= 60.84π

= 191 cm^2 (to 3 s.f.)

And that’s all for today, students! Math Lobby hopes that after this article, you have a clear understanding on spheres, their formulae and its application!

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