EXAMPLE 3 Use trigonometry to find the volume

EXAMPLE 4 Find volume of a composite solid Find the volume of the solid

EXAMPLE 4 Find volume of a composite solid = 216 + 72 Simplify. =

EXAMPLE 5 Solve a multi-step problem SCIENCE You are using the funnel shown to

EXAMPLE 5 Solve a multi-step problem SOLUTION STEP 1 Find: the volume of the

EXAMPLE 5 Solve a multi-step problem STEP 2 Divide: the volume of the funnel

GUIDED PRACTICE for Examples 3, 4 and 5 4. Find the volume of the

GUIDED PRACTICE for Examples 3, 4 and 5 5. A right cylinder with radius

GUIDED PRACTICE for Examples 3, 4 and 5 6. What If? In Example 5,

Slides: 10

Download presentation

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. opp. Write ratio. tan 65° = Adj. tan 65° = 16 r= ≈ 7. 46 tan 65° Substitute. Solve for r.

EXAMPLE 3 Use trigonometry to find the volume of a cone Use the formula for the volume of a cone. 1 V= 3 (π r 2)h 1 ≈ 3 π(7. 462)(16) ≈ 932. 45 ft 3

EXAMPLE 4 Find volume of a composite solid Find the volume of the solid shown. SOLUTION 1 = s 3 + 3 Bh Write formulas. = 63 + 1 (6)2 6 3 Substitute.

EXAMPLE 4 Find volume of a composite solid = 216 + 72 Simplify. = 288 Add. ANSWER The volume of the solid is 288 cubic meters.

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 m. L = 1 cm 3)

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 = 1 (πr 2)h 3 1 = 3 π(42)(6) ≈ 101 cm 3 = 101 m. L

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 m. L ≈ 36. 07 m. L/s 2. 8 s ANSWER The flow rate of the sand is about 36. 07 milliliters per second.

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. ANSWER v= 1 1 2 2 (5. 8) ≈ 143. 92 in 3 (π r )h ≈ π (4. 87) 3 3

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. ANSWER 330 cm 2

GUIDED PRACTICE for Examples 3, 4 and 5 6. 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. ANSWER 101 ml = 31. 56 ml/s 3. 25