7.6

What’s the Relationship?

pg. 16Surface Area and Volume of a Sphere

7.6 – What Is The Relationship?Surface Area and Volume of Spheres

This lesson will complete the three-dimensional formulas. You will learn about a new shape that you encounter often in your daily life: a sphere. You will also make connections between a cylinder, a cone, and a sphere with the same radius and height.

7.28 – BUBBLESAlonzo was blowing bubbles to amuse his little sister. He wondered, "Why are bubbles always perfectly round?“

a. Discuss Alonzo's question with the class. Why are free-floating bubbles always shaped like a perfectly round ball?

Equal pressure pushing on all sides

b. The shape of a bubble is called a sphere. What other objects are shaped like a sphere?

Baseball, basketball, globe

c. What shape two-dimensional shape is related to spheres?

circle

7.29 – SURFACE AREA OF A SPHEREAlonzo was interested in finding the surface area of a sphere. He noticed that when he wrapped a cylinder around a sphere, it has the same surface area. Assume the length and height are the same for the cylinder and sphere. Find the surface area of the sphere, given the radius of r.

22 2cylinderSA r rH

2sphereSA rH 2 2sphereSA r r24sphereSA r video

7.30 – SURFACE AREA OF A SPHEREFind the surface area of the following spheres. Show all work. Leave answers in terms of pi.

24SA r

24 3SA 236SA cm

24SA r 24 9SA

2324SA mm

7.31 – VOLUME OF A SPHEREAlonzo was interested in finding the volume of a sphere. He filled a sphere full of water. Then he placed it into a cylinder with the same height. He noticed that it took 2/3 the volume of the cylinder. Find the formula for the volume of a sphere.

2cylinderV r H

222

3sphereV r r

34

3sphereV r

video

7.32 –VOLUME OF A SPHEREUsing what you have learned, find the volume of the spheres.

34

3V r

343

3V

336V cm

34

3V r

349

3V

3972V mm

2SA B PH V BH

22 2SA r rH 2V r H

1

2SA B P 1

3V BH

2SA r r 21

3V r H

24SA r

34

3V r