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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: - PowerPoint PPT Presentation
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EXAMPLE 1 Find the number of unit cubes
3- D PUZZLE Find the volume of the puzzle piece in cubic units.
EXAMPLE 1
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 is14 + 4 + 2 = 20 cubic units.
Find the number of unit cubes
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 12
= 30cm2 and h = 5 cm.
V = Bh = 30(5) = 150cm3
EXAMPLE 2 Find volumes of prisms and cylinders
b. Right cylinder
SOLUTION
b. The area of the base is
V = Bh = 81π(6) = 486π ≈ 1526.81 ft3
π 92, or 81πft2. Use h = 6 ft to find the volume.
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
90 in3. = x3
4.48 in. ≈ x
Formula for volume of a cube
Substitute for V.
Find the cube root.
GUIDED PRACTICE for Example 1,2,and 3
1. 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
= 7
SOLUTION
The volume of the puzzle cube is 7 units3
To find the volume, find the number of unit cubes it contains. Separate the piece into three rectangular boxes as follows
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
GUIDED PRACTICE for Example 1,2,and 3
3. The volume of a right cylinder is 684π cubicinches 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 = 68418
r = 38 Simplify
The radius of a right cylinder is in 38