Warm Up

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## Warm Up

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**Discovery**• http://www.learner.org/courses/learningmath/measurement/session8/part_b/cylinders.html**Formula’s**• V = (1/3)Bh • Where B is the area of the base and h is the height**1**a. V = Bh 3 1 1 = ( 4 6)(9) 3 2 EXAMPLE 1 Find the volume of a solid Find the volume of the solid. = 36 m3**b.**1 V = Bh 3 1 = (πr2)h 3 1 = (π 2.22)(4.5) 3 EXAMPLE 1 Find the volume of a solid = 7.26π ≈ 22.81 cm3**1**V = bh 3 1 2,226,450 = (x2)(144) 3 EXAMPLE 2 Use volume of a pyramid ALGEBRA Originally, the pyramid had height 144 meters and volume 2,226,450 cubic meters. Find the side length of the square base. SOLUTION Write formula. Substitute.**ANSWER**Originally, the side length of the base was about 215meters. EXAMPLE 2 Use volume of a pyramid 6,679,350 = 144x2 Multiply each side by 3. 46,384 ≈ x2 Divide each side by 144. 215 ≈ x Find the positive square root.**ANSWER**152.42 yd3 for Examples 1 and 2 GUIDED PRACTICE Find the volume of the solid. Round your answer to two decimal places, if necessary. 1. Hexagonal pyramid**2. Right cone**ANSWER 163.49m3 for Examples 1 and 2 GUIDED PRACTICE**ANSWER**The Height of the cone is 12.5m for Examples 1 and 2 GUIDED PRACTICE 3. The volume of a right cone is 1350πcubic meters and the radius is 18meters. Find the height of the cone.**Find the volume of the right cone.**To find the radius r of the base, use trigonometry. opp. tan 65° = Adj. 16 tan 65° = r 16 r = tan 65° EXAMPLE 3 Use trigonometry to find the volume of a cone SOLUTION Write ratio. Substitute. ≈ 7.46 Solve for r.**1**1 V = (π r 2)h ≈ π(7.462)(16) ≈ 932.45 ft3 3 3 EXAMPLE 3 Use trigonometry to find the volume of a cone Use the formula for the volume of a cone.**Find the volume of the solid shown.**1 1 = s3 + Bh 3 3 = 63 + (6)2 6 EXAMPLE 4 Find volume of a composite solid SOLUTION Write formulas. Substitute.**ANSWER**The volume of the solid is 288cubic meters. EXAMPLE 4 Find volume of a composite solid = 216 + 72 Simplify. = 288 Add.**Homework**• Pg. 832-833 • 3-25 odd