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
Figure — use these to answer the problems
- Diameter6 cm
- Circumference18.85 cm
- Area28.27 cm²
- Circumference ÷ diameter3.14
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsFrom “Distance Between Two Points”
From (0, 0) to (8, 15). Distance?
AnswerFrom “The Pythagorean Theorem”
Legs 9 and 12. Hypotenuse?
AnswerFrom “Placing an Irrational Number”
√40 lies between which two whole numbers? Give the smaller.
Answer
Warm Up
Straightforward practice. Get the method working first.
3 problemsA cylinder holds 210. Its matching cone holds?
AnswerA cylinder holds 90. Its matching cone holds?
AnswerRadius 4. What is r³?
Answer
Build It Up
The same ideas with more to keep track of.
2 problemsDiameter 10. What radius goes into the formula?
AnswerHow many cones of the same base and height fill one cylinder?
Answer
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?
AnswerThe Cone
A cylinder holds 300. A cone with the same base and height holds how much?
Answer