1. Use trigonometry to find the volume of a cone
EXAMPLE 3
Use trigonometry to find the volume of a cone
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.

2. EXAMPLE 3
Use trigonometry to find the volume of a cone
Use the formula for the volume of a cone.
V = (π r 2)h ≈ π(7.462)(16) ≈ ft3 3 1

3. Find volume of a composite solid
EXAMPLE 4
Find volume of a composite solid
Find the volume of the solid shown.
SOLUTION
= s Bh 1 3
Write formulas.
= (6)2 6 1 3
Substitute.

4. Find volume of a composite solid
EXAMPLE 4
Find volume of a composite solid =
Simplify.
= 288
Add.
The volume of the solid is 288 cubic meters.
ANSWER

5. EXAMPLE 5
Solve a multi-step problem
SCIENCE
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)

6. EXAMPLE 5
Solve a multi-step problem
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

7. EXAMPLE 5
Solve a multi-step problem
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.
ANSWER

8. To find the radius r of the base, use triangle.
GUIDED PRACTICE
for Examples 3, 4 and 5
4. Find the volume of the cone at the right. Round your answer to two decimal places.
SOLUTION
To find the radius r of the base, use triangle.
tan 40° =
opp.
Adj.
Write ratio.
tan 65° = r
5.8
Substitute.
5.8 tan 40° = 4.87
Solve for r.

9. GUIDED PRACTICE
for Examples 3, 4 and 5
Use the formula for the volume of a cone
v = (π r 2)h ≈ π (4.87)2 (5.8) ≈ in3 3 1

10. GUIDED PRACTICE
for Examples 3, 4 and 5
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.
SOLUTION
Volume of solid
Volume of cylinder
Volume of cone = +
= π 32 h (πr2) h 3 1
= π (π32) 5 3 1
= 330 cm2

11. GUIDED PRACTICE
for Examples 3, 4 and 5
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.
SOLUTION
Divide the volume of the funnel by the time it takes the sand to empty out of the funnel.
101ml
3.25 =
31.56ml/s