Lesson 11: Rectangular Prisms and Volume CE 2015 Math 6 B Unit 3: Geometry and Measurement
volume
the amount of space an object takes up
cubic unit
A unit such as a cubic meter to measure volume or capacity.
To use the formula for finding the volume of a rectangular prism, substitute the value of each dimension into the formula, and then multiply the three values. Remember that the units will be cubed because volume is a three-dimensional measurement. Find the volume of the figure. A rectangular prism has length of 3.2, width of 2, and height of 12.4 millimeters, and the volume of the prism is calculated using these values. In addition to the prism, three equations are shown. First: V equals l times w times h; Write the formula. Second: V equals left-parenthesis 3.2 right-parenthesis left-parenthesis 2 right-parenthesis left-parenthesis 12.4 right-parenthesis; Substitute the given values. Third: V equals 79.36 millimeters cubed; Multiply. Find the volume of a rectangular prism with the given dimensions by following these steps: Write the formula. Substitute the given values. Multiply the three values and record the cubic units. Dimensions length: 6.5 ft width: 2 ft height 3.5 ft Click on the Show Answer button to review your answer. Show Answer What is the volume of a rectangular prism with a length of 12 cm, a width of 30 cm, and a height of 4 cm? Click on the Show Answer button to review your answer. Show Answer Now you can solve the problem from the beginning of the lesson. The dimensions of the current box are 8 inches by 3 inches by 10 inches. What could the dimensions of the new box be to maintain the current volume? Which box dimensions would have the same volume as the original box? Box A: 12 in. × 2 in. × 10 in. OR Box B: 6 in. × 5 in. × 8 in. Click on the Show Answer button to review your answer. Show Answer Click on the link below to watch the "Volume of Rectangular Solids" Teachlet® Tutorial. Pay attention to how to use the formula to find the volume of rectangular prisms. mouse Volume of Rectangular Solids Click on the link below to complete the "Volumes of Rectangular Prisms" activity from the digits™ website. Practice finding the volume of rectangular prisms. Mouse icon Example 1 Mouse icon Volume of a Prism Mouse icon Example 2 Mouse icon Example 3 CA Logo Modification: Click on the links below to complete the alternate activities. First complete pp. 494-498 of the Homework Helper, and then pp. 354-355 of the Student Companion. Mouse icon Homework Helper Mouse icon Stude
To use the formula for finding the volume of a rectangular prism, substitute the value of each dimension into the formula, and then multiply the three values. Remember that the units will be cubed because volume is a three-dimensional measurement. Find the volume of the figure. A rectangular prism has length of 3.2, width of 2, and height of 12.4 millimeters, and the volume of the prism is calculated using these values. In addition to the prism, three equations are shown. First: V equals l times w times h; Write the formula. Second: V equals left-parenthesis 3.2 right-parenthesis left-parenthesis 2 right-parenthesis left-parenthesis 12.4 right-parenthesis; Substitute the given values. Third: V equals 79.36 millimeters cubed; Multiply. Find the volume of a rectangular prism with the given dimensions by following these steps: Write the formula. Substitute the given values. Multiply the three values and record the cubic units. Dimensions length: 6.5 ft width: 2 ft height 3.5 ft Click on the Show Answer button to review your answer. Show Answer Answer: V equals l times w times h V equals 6.5 times 2 times 3.5 V equals 45.5 feet cubed The volume of the rectangular prism is 45.5 cubic feet. What is the volume of a rectangular prism with a length of 12 cm, a width of 30 cm, and a height of 4 cm? Click on the Show Answer button to review your answer. Show Answer Answer: The volume of the prism is 1,440 cubic centimeters. V = lwh V = (12)(30)(4) V = 1,440 cm3 Now you can solve the problem from the beginning of the lesson. The dimensions of the current box are 8 inches by 3 inches by 10 inches. What could the dimensions of the new box be to maintain the current volume? Which box dimensions would have the same volume as the original box? Box A: 12 in. × 2 in. × 10 in. OR Box B: 6 in. × 5 in. × 8 in. Click on the Show Answer button to review your answer. Show Answer Answer: Box A and Box B would both work because they each have a volume of 240 cubic inches. Box A Box B V= lwh V= lwh V= (12)(2)(10) V= (6)(5)(8) V= 240 V= 240 Click on the link below to watch the "Volume of Rectangular Solids" Teachlet® Tutorial. Pay attention to how to use the formula to find the volume of rectangular prisms. mouse Volume of Rectangular Solids Click on the link below to complete the "Volumes of Rectangular Prisms" activity from the digits™ website. Practice finding the volume of rectangular prisms. Mouse icon Example 1 Mouse icon Volume of a Prism Mouse icon Example 2 Mouse icon Example 3 CA Logo Modification: Click on the links below to complete the alternate activities. First complete pp. 494-498 of the Homework Helper, and then pp. 354-355 of the Student Companion. Mouse icon Homework Helper Mouse icon Stude
