Lesson 3
1. Lesson 3
1.13. Connect
Module 7: Volume and Capacity
Connect
Going Beyond
There is a clever way to determine the formula for the volume of a sphere from the formulas for the area of a sphere and the volume of a cone.
Take a little circular patch of area B1 on the surface of the sphere and form a cone by linking B1 to the centre of the sphere.
The volume of this small cone is V1.
Use the formula for the volume of a cone, 
, since the height of the cone is the radius of the sphere.
Take a second patch, B2, and form a second cone. The volume is 
.
Keep following this procedure until you have covered the entire surface of the sphere with little patches.
The volume of the sphere will be the sum of all the volumes of these little cones.
But B1 + B2 + B3 +… is simply the surface area of the sphere given by 4 × π × r2. So, substitute,
Project Connection
You are now ready to complete Step 9 of the Module 6/7 Project: Clear The Roads!
Remember to save all your work to your course folder to submit at the end of the module.
Lesson 3 Assignment
Your lesson assignment contains some problems for you to solve using the knowledge gained during the lesson. Now you will have the chance to apply the concepts and strategies learned to a new situation. Please show work to support your answers.
Open the Lesson 3 Assignment that you saved to your course folder and complete the questions.