8
EXAMPLE 1 Find the number of unit cubes 3- D PUZZLE Find the volume of the puzzle piece in cubic units.

EXAMPLE 1

Embed Size (px)

DESCRIPTION

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

Citation preview

Page 1: EXAMPLE 1

EXAMPLE 1 Find the number of unit cubes

3- D PUZZLE Find the volume of the puzzle piece in cubic units.

Page 2: EXAMPLE 1

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

Page 3: EXAMPLE 1

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

Page 4: EXAMPLE 1

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.

Page 5: EXAMPLE 1

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.

Page 6: EXAMPLE 1

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

Page 7: EXAMPLE 1

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

Page 8: EXAMPLE 1

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