1. Volume of Pyramids and Cones
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm-Up
Find the area of each polygon or circle.
1. Regular hexagon, side length 9 in.
ANSWER
in.2
2. Circle, radius 15 m
ANSWER m2
3. Right triangle, hypotenuse 12 cm, side length 6 cm
ANSWER
31.18 cm

3. Warm-Up
4. Solve
x =
(2 3 )2 3 12
ANSWER 15

4. Example 1
Find the volume of the solid. a.
V = Bh 1 3
= ( )(9) 1 3 2
= 36 m3

5. Example 1
Find the volume of the solid. b.
V = Bh 1 3
= (π )(4.5) 1 3
= 7.26π
≈ cm3

6. Originally, the side length of the base was about 215 m.
Example 2
Originally, the pyramid had height 144 meters and volume 2,226,450 cubic meters. Find the side length of the square base.
ALGEBRA
SOLUTION
V = bh
Write formula.
2,226,450 = (x2)(144)
Substitute.
6,679,350 = 144x2
Multiply each side by 3.
46,384 ≈ x2
Divide each side by 144.
215 ≈ x
Find the positive square root.
Originally, the side length of the base was about 215 m.

7. Guided Practice
Find the volume of the solid. Round your answer to two decimal places, if necessary.
1. Hexagonal pyramid
yd3
ANSWER

8. Guided Practice
Find the volume of the solid. Round your answer to two decimal places, if necessary.
2. Right cone m3
ANSWER

9. Guided Practice
3. The volume of a right cone is 1350π cubic meters and the radius is 18 meters. Find the height of the cone.
12.5 m
ANSWER

10. Find the volume of the right cone.
Example 3
Find the volume of the right cone.
SOLUTION
To find the radius r of the base,
use trigonometry.
tan 65° =
opp.
Adj.
Write ratio.
tan 65° = 16 r
Substitute.
r =
tan 65° 16
≈ 7.46
Solve for r.

11. Example 3
Use the formula for the volume of a cone.
V = (π r 2)h ≈ π(7.462)(16) ≈ ft3 3 1

12. Find the volume of the solid shown.
Example 4
Find the volume of the solid shown.
SOLUTION
= s Bh 1 3
Write formulas.
= (6)2 6 1 3
Substitute. =
Simplify.
= 288
Add.
The volume of the solid is 288 cubic meters.

13. Example 5
You are using the funnel shown to measure the coarseness of a particular type of sand. It takes 2.8 seconds for the sand to empty out of the funnel. Find the flow rate of the sand in milliliters per second. (1 mL = 1 cm3)
SCIENCE
SOLUTION
STEP 1
Find the volume of the funnel using the formula for the volume of a cone.
V = (πr2)h 1 3
= π(42)(6) 1 3
≈ 101 cm3
= 101 mL

14. Example 5
STEP 2
Divide the volume of the funnel by the time it takes the sand to empty out of the funnel.
101 mL
2.8 s
≈ mL/s
The flow rate of the sand is about milliliters per second.

15. Guided Practice
4. Find the volume of the cone at the right. Round your answer to two decimal places.
in3
ANSWER

16. Guided Practice
5. A right cylinder with radius 3 centimeters and
height 10 centimeters has a right cone on top of it with the same base and height 5 centimeters. Find the volume of the solid. Round your answer to two decimal places.
330 cm2
ANSWER

17. Guided Practice
WHAT IF? In Example 5, suppose a different type of sand is used that takes 3.2 seconds to empty out of the funnel. Find its flow rate. 6.
101ml
3.25 =
31.56 ml/s
ANSWER

18. Lesson Quiz
Find the volume of each solid. 1.
ANSWER
96 in.3

19. Lesson Quiz
Find the volume of each solid. 2.
ANSWER
mm3

20. Lesson Quiz
3. Find the volume of the cube after the cone is
removed.
ANSWER
mm3

21. Lesson Quiz
4. Find the volume of a right cone with height
32 in. and radius r in. is in.3. Find r.
ANSWER
8.0 in.