Volume of Prisms
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1. The document discusses how to calculate the volume of prisms. Volume is the number of cubic units needed to fill a space, and a cubic unit is the space occupied by a cube of unit measure. 2. The volume of a prism can be calculated using the formula V = Bh, where B is the area of the base and h is the height of the prism. 3. Examples are provided to demonstrate calculating the volume of rectangular and triangular prisms using measurements of the base and height.
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1. The document is a lesson on calculating volume for rectangular prisms and triangular prisms. It provides the formulas for volume (V=l×w×h for rectangles, V=B×h for triangles where B is the area of the base) and examples of using the formulas.
2. Students are asked to practice calculating volumes of different shapes using the given formulas and by finding the area of various bases for triangular prisms.
3. The lesson defines key terms like volume and provides the volume formulas to use for different shapes.
Volume of Prisms
Rectangular and triangular prisms have formulas to calculate their volume (V).
For a rectangular prism, V = (bh)h, where b is the width, h is the height, and the product bh gives the area of the rectangular base.
For a triangular prism, V = (1/2)bh, where b is the base, h is the height. The area of the triangular base is calculated as (1/2)bh.
Both formulas multiply the area of the base by the height to determine the volume of the entire prism.
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This document contains a math lesson on calculating the volume of rectangular prisms. It provides examples of three rectangular prisms with different heights but the same length and width, and has students write expressions for the volume of each. It then has students recognize that these expressions all represent the area of the base multiplied by the height. Students are asked to determine the volumes of additional prisms using this area of base times height formula.
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This document provides examples and problems about calculating the volume of rectangular prisms. It begins by showing different rectangular prisms and having students write expressions for the volume of each using length, width, and height. It explains that the volume can also be written as the area of the base times the height. Students then practice calculating volumes using both methods. Later problems involve calculating volume when given the area of the base and height or vice versa. The goal is for students to understand that the volume of a rectangular prism is the area of its base multiplied by its height.
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Volume of Prisms
- 1. Volume of Prisms 1. Volume – the number of cubic units needed to fill a given space. 2. Cubic unit – space occupied by a cube of unit measure. Ex.1. V = Bh 8 in V =(b h) h 6 in V = 12(6)(8) 12 in V = 576 in³ V = Area of base x height of the prism
- 2. Volume of Prisms Ex.2. b = 2.5 in h = 2.5 in 5 in h = 5 in V = Area of base x Height 2.5 in V = Bh 2.5 in V = bhh V = 2.5(2.5)(5) V = 31.25 in³
- 3. Ex.3. Find the volume of the triangular prism V = Area of base x height 10 in V=Bh 8 in 14 in h = 14 in 6 in bxh 6x8 8 in Area of base B = 2 = 2 6 in = 24 in² V=Bh = 24 (14) = 336 in³
- 4. 10 in What is the relationship between the volume of a triangular prism and a 8 in 14 in rectangular prism? 6 in So, we can use the same formula, but divide it by 2. V= bhh 2 (8)(6)(14) V= 2 V = 336 cubic inches