In these lessons we will learn

### Surface Area of a Sphere

This video shows how to calculate the surface area of a sphere given the radius or diameter.

### Surface Area of a hemisphere

### Problems about surface area of spheres

Problem: What is the radius of the sphere given the surface area?
Problem: The surface area of a sphere is 5024 square meters. What is the volume of the sphere?

Problem: The radius of a sphere is tripled.

a) Describe the effect on the volume.

b) Describe the effect on the surface area.
### Proof of the formula of the surface area of a sphere

This video demonstrates that the surface area of a sphere equals the area of 4 circles. (It is not a formal proof)

The formula for the surface of a sphere is derived by summing up small ring elements of area along its perimeter. (uses calculus)
These two videos explain the Archimedes method of deriving the surface area of a sphere.

Part1:
Part 2:

- the formula of the surface area of a sphere.
- how to calculate the surface area of a sphere.
- how to calculate the surface area of a hemisphere.
- how to solve problems about the surface area of spheres.
- how to prove the formula of the surface area of a sphere.

A **sphere** is a solid in which all the points on the round surface are equidistant from a **fixed point**, known as the center of the sphere. The distance from the center to the surface is the **radius**.

Surface area of a sphere is given by the formula

Surface Area of sphere = 4π

r^{2}

where *r* is the radius of the sphere.

* Example: *

Calculate the surface area of a sphere with radius 3.2 cm

**Solution:**

Surface area of sphere

= 4*π r*^{2}

= 4*π* (3.2)^{2
}= 4 × 3.14 × 3.2 × 3.2

= 128.6 cm^{2}

Worksheet to calculate the surface area of spheres.

The following video shows how to find the surface area of a sphere.A **hemisphere** is half a sphere, with one flat circular face and one bowl-shaped face.

The surface area of a hemisphere is equal to the area of the curve surface plus the area of the circular base.

Surface area of hemisphere

= × surface area of sphere + area of base

= × 4*π **r*^{2} + *π **r*^{2 }= 3*π* *r*^{2}

**Example: **

Calculate the surface area of a hemisphere with radius 4 cm

**Solution:**

Surface area of hemisphere

= × surface area of sphere + area of base

= × 4*π **r*^{2} + *π **r*^{2}

= 3*π* *r*^{2}

= 3*π* (4)^{2}

= 150.86 cm^{2}

Problem: The radius of a sphere is tripled.

a) Describe the effect on the volume.

b) Describe the effect on the surface area.

Part1:

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