EXAMPLE 1 Find the volume of a solid

EXAMPLE 1 Find the volume of a solid Find the volume of the solid. a. V = 13 Bh 1 = 3 ( 1 4 6)(9) 2 = 36 m 3

EXAMPLE 1 Find the volume of a solid b. V = 1 Bh 3 = 13 (πr 2)h = 31 (π 2. 22)(4. 5) = 7. 26π ≈ 22. 81 cm 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 1 V= bh 3 1 2 2, 226, 450 = (x )(144) 3 Write formula. Substitute.

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

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 SOLUTION Volume is v = 1 bh 3 Area of a hexagon of base 4 is 41. 57 1 1 (41. 57)(11) = 152. 42 yd 3 v= bh = 3 3

GUIDED PRACTICE 2. for Examples 1 and 2 Right cone SOLUTION 1 Value of a cone is v = bh 3 First find by Pythagorean method

GUIDED PRACTICE h = (82) – (5)2 = 6. 24 1 v= bh 3 for Examples 1 and 2 Substitute. Simplify Write formula. 1 = (π 52)(6. 24) 3 Substitute. = 163. 49 m 3 Simplify

GUIDED PRACTICE 3. for Examples 1 and 2 The volume of a right cone is 1350π cubic meters and the radius is 18 meters. Find the height of the cone. SOLUTION V = 1 bh 3 Write formula. 1 1350π = 3 (π182)h Substitute. 4050π = π(18)2 h Multiply each side by 3. 12. 5 = h Divide each side by 324 π. ANSWER The Height of the cone is 12. 5 m