Use trigonometry to find the volume of a cone

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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.

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) ≈ 932.45 ft3 3 1

Find volume of a composite solid EXAMPLE 4 Find volume of a composite solid Find the volume of the solid shown. SOLUTION = s3 + Bh 1 3 Write formulas. = 63 + (6)2 6 1 3 Substitute.

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

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)

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

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 ≈ 36.07 mL/s The flow rate of the sand is about 36.07 milliliters per second. ANSWER

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. v = (π r 2)h ≈ π (4.87)2 (5.8) ≈ 143.92 in3 3 1 ANSWER

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. 330 cm2 ANSWER

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. 101ml 3.25 = 31.56 ml/s ANSWER