1. 12.5 Volume of Pyramids and Cones
Chapter 12
12.5
Volume of Pyramids and Cones
GOAL 1
Finding Volumes of Cones
GOAL 2
Using Volumes in Real-Life Problems

2. Find the area of the base of the cone
Base is a circle
Area of Circle = r2
B = 36 in2

3. Theorem 12.9 Volume of a Cone
B is the area of the base
H is the height

4. Find the volume of each cone
Area of the Base
B = r2 = (4)2 = 16
Find the height
h = 12
Fill in the formula

5. Find the volume of each cone
Area of the base
B = r2 = (5)2 = 25
Find the height
From vertex perpendicular to base
h = 82
h = 39
Fill in the formula

6. Find the volume of each cone
Area of the base
B = r2 = (9)2 = 81
Find the height
From vertex perpendicular to base
h = 212
h = 360 = 610
Fill in the formula

7. Applications
To complete a construction job, a contractor needs 145 more cubic yards of concrete. If there remains a conical pile of concrete mix measuring 36 feet in diameter and 12 feet high, is there enough concrete still on the job site to finish the job? Explain your reasoning.
How much does he have? (Find the volume or the pile)
Convert feet to yards d = 12 yds, r = 6 yds, h = 4 yds
Find the Volume
Yes he has plenty

8. Applications
The limestone blocks from which an ancient pyramid was made weigh about 2 tons per cubic yard. Find the approximate weight of the pyramid having a square base of length 250 yards and a height of 150 yards
What is the volume (Use the formula for a pyramid)
Find the weight (Multiply by 2)
(2) = tons

9. Find the volume of the solid
Composed of two cones each with radius of 5.
Need to find the height of each cone.
Find the Volume of each cone
Add the volumes together

10. First, find the volume of the left cone
Find the height (pythagorean theorem)
h = 102  h = 53
Find the Volume

11. Second, find the volume of the right cone
Find the height (pythagorean theorem)
h = 182  h = 299
Find the Volume

12. Now find the total Volume
Volume of left cone: V  in3
Volume of Right Cone: V  in3
Total Volume: V  = in3

13. Homework #67 Pg , 17-19, 21, 25-37, 40-51