In each prism here the base shapes is highlighted. Focusing on triangular and rectangular prisms, create a table like this one and determine the specific formula to calculate the volume of rectangular and triangular prisms. 3 D shape Name of base shape Area formula of base shape General volume formula Specific volume formula of the prism Rectangular prism Volume = Area of base × Height Triangular prism Volume = Area of base × Height

The surface a solid object stands on, or the bottom line of a shape such as a triangle or rectangle is the base of a three dimensional object. A prism is a shape with two identical shapes facing each other. These identical shapes are called base. Here, we have The base of the above prism is triangle. Area of triangle = 1 2 × base × height So, the specific volume formula of the prism = 1 2 × b × h × l Similarly, consider the following rectangular prism, The base of the above prism is rectangle. Area of rectangle = Length × Breadth So, the specific volume formula of the prism = l × b × h So, the complete table is, 3 D shape Name of base shape Area formula of base shape General volume formula Specific volume formula of the prism Rectangular prism Rectangle Length × Breadth Volume = Area of base × Height l b h Triangular prism Triangle 1 2 × base × height Volume = Area of base × Height 1 2 l b h

Is a cube a rectangular prism? Can you apply base area × height to determine the formula for calculating the volume of a cube? What would that formula be?

A cube is a three-dimensional shape. All the faces of the cube are in square shape and have equal dimensions. A cuboid is also a polyhedron. The faces of the cuboid are parallel. But not all the faces of a cuboid are equal in dimensions. The main difference between a cube and a cuboid is that a cube has six square-shaped faces of the same size but a cuboid has rectangular faces. So, we can say that rectangular prism is a cuboid with rectangular faces. And, the volume of a cube can be measured by using the formula as, length × breadth × height = a × a × a [ a is the side length of cube, each side equal] So, volume of cube = Side 3

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MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Reflect and discuss 5>Q •

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Earn 100

Explain why the volume of a cube measuring $1 cm$ on each side is $1 {cm}^{3}$ .

Important Questions on Perimeter, Area and Volume Environmental Impacts

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MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Three-dimensional prisms>Q 1

How would you define the 'base' of a prism?

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MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Three-dimensional prisms>Q 2

Marcos says, 'The base is the side that the shapes sits on'. Is Marcos correct? Explain.

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MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Three-dimensional prisms>Q 3

Make a generalization in words about the relationship between the area of a base shape and the volume of its corresponding prism.

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MYP Mathematics A concept-based approach 1>Chapter 7 - Perimeter, Area and Volume Environmental Impacts>Three-dimensional prisms>Q 5

In each prism here the base shapes is highlighted.

Question Image

Focusing on triangular and rectangular prisms, create a table like this one and determine the specific formula to calculate the volume of rectangular and triangular prisms.

$3 D$ shape	Name of base shape	Area formula of base shape	General volume formula	Specific volume formula of the prism
Rectangular prism			Volume $=$ Area of base $\times$ Height
Triangular prism			Volume $=$ Area of base $\times$ Height