EXAMPLE 1 Find the number of unit cubes 3- D PUZZLE

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Presentation transcript:

EXAMPLE 1 Find the number of unit cubes 3- D PUZZLE Find the volume of the puzzle piece in cubic units.

EXAMPLE 1 Find the number of unit cubes SOLUTION To find the volume, find the number of unit cubes it contains. Separate the piece into three rectangular boxes as follows: The base is 7 units by 2 units. So, it contains 7 . 2, or 14 unit cubes. The upper left box is 2 units by 2 units. So, it contains 2 . 2, or 4 unit cubes. The upper right box is 1 unit by 2 units. So, it contains 1 . 2, or 2 unit cubes. By the Volume Addition Postulate, the total volume of the puzzle piece is 14 + 4 + 2 = 20 cubic units.

EXAMPLE 2 Find volumes of prisms and cylinders Find the volume of the solid. a. Right trapezoidal prism SOLUTION (3)(6 + 14) a. The area of a base is 1 2 = 30cm2 and h = 5 cm. V = Bh = 30(5) = 150cm3

EXAMPLE 2 Find volumes of prisms and cylinders SOLUTION b. Right cylinder b. The area of the base is π 92, or 81πft2. Use h = 6 ft to find the volume. V = Bh = 81π(6) = 486π ≈ 1526.81 ft3

The volume of the cube is 90 cubic inches. Find the value of x. EXAMPLE 3 Use volume of a prism ALGEBRA The volume of the cube is 90 cubic inches. Find the value of x. SOLUTION A side length of the cube is x inches. V = x3 Formula for volume of a cube 90 in3. = x3 Substitute for V. 4.48 in. ≈ x Find the cube root.

GUIDED PRACTICE for Example 1,2,and 3 1. Find the volume of the puzzle piece shown in cubic units. SOLUTION To find the volume, find the number of unit cubes it contains. Separate the piece into three rectangular boxes as follows The volume of the puzzle cube = lbh = (1)(1)(1) + (2)(1)(3) = 1 + 6 = 7 The volume of the puzzle cube is 7 units3

GUIDED PRACTICE for Example 1,2,and 3 2. Find the volume of a square prism that has a base edge length of 5 feet and a height of 12 feet. SOLUTION The volume of a square prism = r2h = 52 (12) = 25 . 12 = 300 The volume of a square prism is 300 ft3

3. The volume of a right cylinder is 684π cubic GUIDED PRACTICE for Example 1,2,and 3 3. The volume of a right cylinder is 684π cubic inches and the height is 18 inches. Find the radius. SOLUTION The volume of a right cylinder is = πr2h 684π = π r2 18 Substitute the value of V. 684 = r2 18 Divide by π on both side r2 = 684 18 r = 38 Simplify The radius of a right cylinder is in 38