A&W Math 11 Chapter 3 Measurement Name:__________________



A&W Math 11 Unit 1 Measurement Name:__________________

Lesson Notes 1.4. Surface Area: Spheres Date:_________________

Today we look at the fascinating sphere. Of all the shapes, a sphere has the smallest surface area for a volume. Or put another way it can contain the greatest volume for a fixed surface area.

The sphere appears in nature whenever a surface wants to be as small as possible, for example bubbles and water drops such as rain.

Here are some other interesting things to notice about spheres:

1) It is perfectly symmetrical

2) It has no edges or vertices, it is not a polyhedron

3) All points on the surface are the same distance from the center

For astronomical bodies such as the planet Earth, is an example of a very large sphere.

A sphere is divided into two equal hemispheres by any plane that passes through its center.

Now let’s look at the formula for surface area of Spheres that will help us find some important quantities.

The Surface Area of a Sphere with radius r is given by

SA = 4 π r2

If we know the radius, we can find the surface area or volume.

If we know the surface area or volume, we can find the radius.

You will have several types of problems. The first is when you are given the radius, you will find the surface area like the following examples.

Example 1) You and your friends are on Spring Break playing with a beach ball. Your “mathy” friend asks, “Hey, how much vinyl makes up this ball?” Your friend is simply inquiring about the sphere’s surface area.

Let’s assume the ball’s diameter is 3 feet.

Example 2) After a game of beach ball, Jenna replenishes her electrolytes by peeling and eating a delicious orange. When she is done, relaxing in the cool spring breeze, she calculates the amount of orange peeling from her snack to be roughly 80 square inches. Now she wants to know what the radius of her orange was!

Example 3) An official NBA basketball has a circumference of 29.5 in. How much leather, to the nearest square inch, is needed for the surface?

Example 4) Find the surface area of the following figures.

[pic]

A&W Math 11 Unit 1 Measurement Name:__________________

Assignment 1.4: Surface Area: Spheres Date:_________________

1) Find the surface area of a volley ball with a diameter of 26 cm.

2) The circumference of a spherical gas storage tank is 50 m. What is the surface area of

the tank?

3) Cool Globes is a project designed to raise awareness of global warming. Artists decorate white globes to show ways to protect the environment. Each globe has a diameter of 5 ft. What area needs to be decorated for each sphere?

4) Jacques claims that another formula for surface area of a sphere is SAsphere = πd 2

• Is he correct? Justify your decision.

5) Sarah is installing security cameras. Each security camera is a sphere. The camera's surface area is 12.5 sq in. What is its diameter?

6) Maurice is an interior designer. He sees this spherical light fixture that costs $40. Maurice wants to use a spherical light fixture with triple the radius of this one. What would be a fair price for it?

7) Find the surface area of the following figures.

[pic]

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