EXAMPLE 1Find the number of unit cubes3- D PUZZLEFind the volume of the puzzle piece in cubic units.

EXAMPLE 1SOLUTIONTo 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 is14 + 4 + 2 = 20 cubic units.Find the number of unit cubes

EXAMPLE 2Find volumes of prisms and cylindersFind the volume of the solid.a. Right trapezoidal prismSOLUTIONV = Bh = 30(5) = 150cm3

EXAMPLE 2Find volumes of prisms and cylindersb. Right cylinderSOLUTIONb. The area of the base isV = Bh = 81(6) = 486 1526.81 ft3

EXAMPLE 3Use volume of a prism

ALGEBRAThe volume of the cube is 90 cubic inches. Find the value of x.SOLUTIONA side length of the cube is x inches.V = x390 in3. = x34.48 in. xFormula for volume of a cubeSubstitute for V.Find the cube root.

GUIDED PRACTICEfor Example 1,2,and 31. Find the volume of the puzzle piece shown in cubic units. The volume of the puzzle cube = lbh= (1)(1)(1) + (2)(1)(3)

= 1 + 6= 7SOLUTIONThe volume of the puzzle cube is 7 units3To find the volume, find the number of unit cubes it contains. Separate the piece into three rectangular boxes as follows

GUIDED PRACTICEfor Example 1,2,and 32. Find the volume of a square prism that has a base edge length of 5 feet and a height of 12 feet.SOLUTIONThe volume of a square prism = r2h= 52 (12)= 25 . 12 = 300The volume of a square prism is 300 ft3

GUIDED PRACTICEfor Example 1,2,and 33. The volume of a right cylinder is 684 cubicinches and the height is 18 inches. Find the radius.SOLUTIONThe volume of a right cylinder is = r2h684 = r2 18Substitute the value of V.684 = r2 18Divide by on both sideSimplify