# VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

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1 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 (cm 3 ) is a cube whose edges all measure 1 centimeter. Examples: Find the volume of each rectangular prism. Round to the nearest tenth if necessary Find the volume of a fish tank that is 8 feet long and 5 feet wide, if the height is 5.5 feet?

2 You try!! 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.

3 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 (cm 3 ) or cubic inches (in 3 ). The volume of the figure at the right can be shown using cubes. } The bottom layer, or base, has 4 3 or 12 cubes. two There are 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 Bh or V wh Find the volume of the rectangular prism. V wh Volume of a rectangular prism V Replace with 5, w with 6, and h with 8. V 240 Multiply. The volume is 240 cubic inches. 6 in. 5 in. 8 in. Find the volume of each rectangular prism. Round to the nearest tenth if necessary m 9 cm 10 cm 7 cm 2.7 ft 3 ft 2 ft Glencoe/McGraw-Hill 674 Mathematics: Applications and Concepts, Course 2

4 NAME DATE PERIOD Practice: Skills Volume of Rectangular Prisms Find the volume of each rectangular prism. Round to the nearest tenth if necessary cm 10 in. 5 in. 6 in. 6 m mm 9.5 in. 9 cm m 5 mm 7 in. ` 2.8 in. 7.2 cm Lesson ft 4.5 cm ft 4 ft 9.6 in. 4.8 in. 15 in. 1.5 cm 1.2 cm Glencoe/McGraw-Hill 675 Mathematics: Applications and Concepts, Course 2

5 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.

6 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!

7 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 2 w 2 h 2wh Find the surface area of the rectangular prism. 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: top and bottom front and back two sides Faces Area top and bottom (4 3) (4 3) 24 front and back (4 2) (4 2) 16 two sides (2 3) (2 3) 12 Sum of the areas Alternatively, replace with 4, w with 3, and h with 2 in the formula for surface area. S 2 w 2 h 2wh Follow order of operations So, the surface area of the rectangular prism is 52 square meters. 2 m 2 m back 2 m side bottom side front top 2 m Find the surface area of each rectangular prism cm 2 in. 8 in. 10 in. 9 ft 5 ft 7 ft Glencoe/McGraw-Hill 684 Mathematics: Applications and Concepts, Course 2

8 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 cm 12 cm 6 cm 7 ft 1 ft 4 ft 9 in. 7 in. 15 in in. 10 mm 9 mm 9 mm 8.5 cm 6 in. 4.3 in. 4 cm in ft 8.3 in. 4.5 in. 6.m 7 ft 12 ft 4.1 mm 7.m 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. Lesson 12 4 Glencoe/McGraw-Hill 685 Mathematics: Applications and Concepts, Course 2

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