Math 6 NOTES 7.5
Name _____________________________________
VOLUME of Rectangular Prisms
•
Volume is the measure of _________________________ occupied by a solid region.
**The formula for the volume of a rectangular prism is:**
_______________________________________________
l = length
w = width
h = height
Study Tip:
When measuring volume, the units will be “cubed.” A cubic
centimeter (cm3) is a cube whose edges all measure 1 centimeter.
Examples:
Find the volume of each rectangular prism. Round to the nearest tenth if necessary.
1.
2.
3. Find the volume of a fish tank that is 8 feet long and 5 feet wide, if the
height is 5.5 feet?
You try!!
1.
2.
3.
4.
5. A rectangular prism measuring 10 m and 7 m along the base and 12 m tall.
6. A square prism measuring 6 km along each edge of the base and 5 km tall.
7. A cube measuring 9 in along each edge.
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention
Volume of Rectangular Prisms
The volume of a solid is the measure of space occupied by it. It
is measured in cubic units such as cubic centimeters (cm3) or cubic
inches (in3). The volume of the figure at the right can be shown
using cubes.
3m
4m
The bottom layer,
or base, has 4 ? 3 ➝
or 12 cubes.
➝
}
There are
two layers.
It takes 12 ? 2 or 24 cubes to fill the box. So, the volume of the box is 24 cubic meters.
A rectangular prism is a solid figure that has two parallel and congruent sides, or bases, that are
rectangles. To find the volume of a rectangular prism, multiply the area of the base and the height, or
find the product of the length ,, the width w, and the height h.
V 5 Bh or V 5 ,wh
Find the volume of the rectangular prism.
V 5 ,wh
Volume of a rectangular prism
V55?6?8
Replace , with 5, w with 6, and h with 8.
V 5 240
Multiply.
8 in.
6 in.
The volume is 240 cubic inches.
5 in.
Find the volume of each rectangular prism. Round to the nearest
tenth if necessary.
1.
2.
4m
3.
3m
2 ft
9 cm
2.7 ft
7m
7 cm
3 ft
10 cm
© Glencoe/McGraw-Hill
674
Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Skills
Volume of Rectangular Prisms
Find the volume of each rectangular prism. Round to the nearest
tenth if necessary.
1.
2.
3.
10 in.
3 cm
4m
7 cm
6m
6 in.
3 cm
5 in.
4.
4m
5.
6.
12 mm
9 cm
9.5 in.
3 cm
7 in.
2.8 in.
5 mm
Lesson 12–2
3 mm
7.2 cm
`
7.
8.
9.
3
4.5 cm
4 4 ft
9.6 in.
15 in.
1
2 2 ft
4 ft
© Glencoe/McGraw-Hill
1.2 cm
4.8 in.
675
1.5 cm
Mathematics: Applications and Concepts, Course 2
Math 6 NOTES 7.4
Name _____________________________________
Notes: Surface Area of Rectangular Prisms & Cubes
•
The sum of the areas of all the surfaces, or _______________, contained in a
three-dimensional figure (solid) is called the __________________________.
- Rectangular prisms are made up of 6 rectangular faces.
- We have to find the areas of all six faces.
- Then add them together to find the surface area of the solid.
**The formula for the Surface Area of a RECTANGULAR PRISM is:**
l = length
w = width
h = height
Examples: Find the surface area of each rectangular prism.
You Try!! Find the surface area of each rectangular prism.
1)
2)
4)
How would you find the surface area of a Pyramid?
•
A square-based Pyramid is made up of five faces:
four triangles and one square.
•
Find the area of these shapes and add them together!
NAME ________________________________________ DATE ______________ PERIOD _____
Study Guide and Intervention
Surface Area of Rectangular Prisms
The sum of the areas of all the surfaces, or faces, of a three-dimensional figure is the surface area.
The surface area S of a rectangular prism with length ,, width w, and height h is found using the
following formula.
S 5 2,w 1 2,h 1 2wh
Find the surface area of the rectangular prism.
2m
You can use the net of the rectangular
prism to find its surface area. There are
three pairs of congruent faces in a
rectangular prism:
d
d
d
4m
3m
back
side
Area
top and bottom
(4 ? 3) 1 (4 ? 3) 5 24
front and back
(4 ? 2) 1 (4 ? 2) 5 16
two sides
(2 ? 3) 1 (2 ? 3) 5 12
Sum of the areas
24 1 16 1 12 5 52
4m
2m
top and bottom
front and back
two sides
Faces
2m
bottom
2m
front
3m
top
side
3m
4m
Alternatively, replace , with 4, w with 3, and h with 2 in the formula for surface area.
S 5 2,w 1 2,h 1 2wh
52?4?312?4?212?3?2
Follow order of operations.
5 24 1 16 1 12
5 52
So, the surface area of the rectangular prism is 52 square meters.
Find the surface area of each rectangular prism.
1.
2.
3.
3 cm
9 ft
10 in.
2 in.
7 cm
8 in.
3 cm
7 ft
5 ft
© Glencoe/McGraw-Hill
684
Mathematics: Applications and Concepts, Course 2
NAME ________________________________________ DATE ______________ PERIOD _____
Practice: Skills
Surface Area of Rectangular Prisms
Find the surface area of each rectangular prism. Round to the
nearest tenth if necessary.
1.
2.
3.
15 in.
7 cm
7 ft
6 cm
12 cm
4 ft
7 in.
1 ft
4.
9 in.
5.
6.
3.7 in.
9 mm
6 in.
10 mm
8.5 cm
4.3 in.
9 mm
4 cm
3 cm
8.
6 ft
9.
4.1 in.
8.3 in.
6.4 mm
4.5 in.
4.1 mm
12 ft
7.3 mm
7 ft
10. A cube has a surface area of 126 square feet. What is the area of one
face?
11. Find the surface area of a rectangular prism that has a length of
8 inches, a width of 3 inches, and a height of 6 inches.
© Glencoe/McGraw-Hill
685
Mathematics: Applications and Concepts, Course 2
Lesson 12–4
7.