Cogito
Grade 8 Math · Chapter 9 · Lesson 3
Volume of Cones, Cylinders, and Spheres
Three solids, three formulas, one radius.
10 problems · about 20 minutes · 8.G.C.9
What this lesson teaches
The child calculates the volume of a cylinder, a cone, and a sphere.
- A cylinder is its base area times its height.
- A cone with the same base and height is one third of that.
- A sphere is 4/3 πr³, and every formula uses the radius.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Distance Between Two Points: From (0, 0) to (8, 15). Distance?
Answer 17
Why 17.
Review — The Pythagorean Theorem: Legs 9 and 12. Hypotenuse?
Answer 15
Why 15.
Review — Placing an Irrational Number: √40 lies between which two whole numbers? Give the smaller.
Answer 6
Why Between 6 and 7.
Warm Up
Straightforward practice. Get the method working first.
3 problemsA cylinder holds 210. Its matching cone holds?
Answer 70
Why 70.
A cylinder holds 90. Its matching cone holds?
Answer 30
Why A third.
Radius 4. What is r³?
Answer 64
Why 4 × 4 × 4.
Build It Up
The same ideas with more to keep track of.
2 problemsDiameter 10. What radius goes into the formula?
Answer 5
Why Halve it.
How many cones of the same base and height fill one cylinder?
Answer 3
Why Each is a third.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Base: A cylinder has radius 5. What is r²?
Answer 25
Why 25.
The Cone: A cylinder holds 300. A cone with the same base and height holds how much?
Answer 100
Why 100.