Volume of Right Prisms and Pyramids in Grade 7

This video tutorial focuses on the volume of right prisms and pyramids. It explains the characteristics of prisms and pyramids, including their bases and faces. The video explores cross sections of 3D objects and how slicing affects their shapes. It provides methods to calculate the volume of prisms by multiplying the base area by the height. The tutorial also covers how to find the base area of complex shapes by decomposing them into simpler polygons. The video concludes with a summary of the key concepts discussed.

What defines a prism in terms of its bases?

• A prism has no bases but only faces.

• A prism has multiple bases of different shapes.

• A prism has two identical bases connected by parallelograms.

• A prism has one base connected by triangles.

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

Which of the following is NOT a characteristic of a pyramid?

• Has two identical bases

• Has one base

• Faces other than the base are triangles

• All faces meet at a single vertex

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CCSS.1.G.A.1

CCSS.2.G.A.1

What is a cross-section in the context of three-dimensional figures?

• A new face seen when the figure is sliced.

• The original face of the figure.

• A new face seen when the figure is rotated.

• The shadow of the figure.

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CCSS.7.G.A.3

What happens to the cross-section of a prism if the slice is parallel to the base?

• It is identical to the base.

• It turns into a different polygon.

• It becomes a circle.

• It becomes a triangle.

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CCSS.7.G.A.3

What is the result of slicing a prism horizontally?

• A cross-section identical to the base

• A cross-section that varies based on the shape of the prism

• A cross-section that is always a triangle

• No cross-section is formed

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CCSS.7.G.A.3

If a prism's base area is 10 square units and its height is 7 units, what is its volume?

• None of the above

• 100 cubic units

• 70 cubic units

• 17 cubic units

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CCSS.7.G.B.6

What is the volume formula for a prism?

• V = length x width x height

• V = base area x height

• V = base perimeter x height

• V = (base area + height) / 2

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CCSS.7.G.B.6

What is the general formula to calculate the volume of a prism?

• Volume = Height / Base Area

• Volume = Base Area + Height

• Volume = Base Area x Height

• Volume = Base Area - Height

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CCSS.7.G.B.6

How can you find the area of a base that has an unusual shape?

• By measuring its perimeter

• By decomposing it into simpler shapes like rectangles and triangles

• By doubling the area of a similar smaller shape

• By calculating its volume and dividing by height

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CCSS.6.G.A.4

How can you decompose an irregular polygon to find its area?

• By calculating the volume and dividing by height

• By subtracting the area of extra pieces from a surrounding rectangle

• By measuring its diameter

• By adding the areas of enclosed circles