## Introduction

- A sphere is a
**rounded**three-dimensional solid**.** - It is perfectly symmetrical.
- All the points on its surface are at an equal distance from its center. This distance is called the radius of the sphere.

- Half of a sphere is called a
**hemisphere.**

## Volume of a Sphere

- If the radius $\left(r\right)$ of a sphere is known, its volume can be found by using the following formula:

$Volum{e}_{sphere}=\frac{4}{3}{\mathrm{\pi r}}^{3}$

- If the diameter $\left(d\right)$ of a sphere is known, its volume can be found by using the following formula:

$Volum{e}_{sphere}=\frac{4}{3}\pi \times {\left(\frac{d}{2}\right)}^{3}$$=\frac{4}{3}\pi \times {\frac{d}{8}}^{3}$$=\frac{1}{6}\pi {d}^{3}$

- The volume of a sphere is measured in

## Surface Area of a Sphere

- The surface area of a sphere is the total area covered by its outer surface.
- If the radius $\left(r\right)$ of a sphere is known, its surface area can be calculated using the formula mentioned below.

$Are{a}_{sphere}=4{\mathrm{\pi r}}^{2}$

## Solved Examples

Question 1: Find the volume of a sphere with a radius of 3 cm.

Solution: **$Volum{e}_{sphere}=\frac{4}{3}{\mathrm{\pi r}}^{3}$****$=\frac{4}{3}\mathrm{\pi}\times {\left(3\right)}^{3}$$=4\mathrm{\pi}\times 9$****$=36\mathrm{\pi}c{m}^{3}$**

Question 2: If the radius of a sphere is 20 cm, find its surface area.

Solution: $Are{a}_{sphere}=4{\mathrm{\pi r}}^{2}$$=4\mathrm{\pi}\times {\left(20\right)}^{2}$$=4\mathrm{\pi}\times 400$$=1600\mathrm{\pi}{\mathrm{cm}}^{2}$

## Cheat Sheet

- $Volum{e}_{sphere}=\frac{4}{3}{\mathrm{\pi r}}^{3}$$=\frac{1}{6}\pi {d}^{3}$
- $Are{a}_{sphere}=4{\mathrm{\pi r}}^{2}$

## Blunder Areas

- The curved surface area and total surface area of a sphere are the same. But the curved surface area and total surface of a hemisphere are not the same.

- Fiona Wong
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