Warm-Up Exercises 1. Regular hexagon, side length 9 in. 2. Circle, radius 15 m ANSWER in. 2 ANSWER m 2 Find the area of each polygon or circle.

Warm-Up Exercises 3. Right triangle, hypotenuse 12 cm, side length 6 cm ANSWER cm Find the area of each polygon or circle. ANSWER Solve x = (2 3 )

Warm-Up Exercises EXAMPLE 1 Find the volume of a solid Find the volume of the solid. V = Bh 1 3 = 36 m 3 a.a. = ( 4 6)(9)

Warm-Up Exercises EXAMPLE 1 Find the volume of a solid V = Bh 1 3 = (πr 2 )h 1 3 = 7.26π ≈ cm 3 b.b. = (π )(4.5) 1 3

Warm-Up Exercises 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 V = bh 1 3 Write formula. 2,226,450 = (x 2 )(144) 1 3 Substitute.

Warm-Up Exercises EXAMPLE 2 Use volume of a pyramid 6,679,350 = 144x 2 Multiply each side by 3. 46,384 ≈ x 2 Divide each side by ≈ x Find the positive square root. Originally, the side length of the base was about 215 meters. ANSWER

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 Find the volume of the solid. Round your answer to two decimal places, if necessary. 1. Hexagonal pyramid yd 3 ANSWER

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 2. Right cone ANSWER m 3

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 3. The volume of a right cone is 1350π cubic meters and the radius is 18 meters. Find the height of the cone. The Height of the cone is 12.5 mANSWER

Warm-Up Exercises EXAMPLE 3 Use trigonometry to find the volume of a cone SOLUTION tan 65° = opp. Adj. Write ratio. Substitute. tan 65° = 16 r r = tan 65° 16 Solve for r. Find the volume of the right cone. To find the radius r of the base, use trigonometry. ≈ 7.46

Warm-Up Exercises 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( )(16) ≈ ft

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

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

Warm-Up Exercises 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 cm 3 )

Warm-Up Exercises 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. ≈ 101 cm 3 = 101 mL V = (πr 2 )h 1 3 = π(4 2 )(6) 1 3

Warm-Up Exercises 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

Warm-Up Exercises 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) ≈ in ANSWER

Warm-Up Exercises 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 cm 2 ANSWER

Warm-Up Exercises 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 ml 3.25 = ml/s ANSWER

Warm-Up Exercises Daily Homework Quiz Find the volume of each solid. 1. ANSWER 96 in. 3

Warm-Up Exercises Daily Homework Quiz 2. ANSWER mm 3

Warm-Up Exercises Daily Homework Quiz ANSWER mm 3 3. Find the volume of the cube after the cone is removed.

Warm-Up Exercises Daily Homework 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.