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6-8 Accelerated 7 Unit 6

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Unit 6

Glossary

Accelerated 7

A base is a specific face of a prism or pyramid.

A prism has 2 identical bases that are parallel. A pyramid has 1 base.

A prism or pyramid is named for the shape of its base.

A pentagonal prism. There are two identical pentagons on the top and bottom. Each vertex of a pentagon is connected by a vertical segment to the corresponding vertex of the other pentagons. The pengatons are each shaded, with the word base pointing to each.

A hexagonal pyramid. There is a hexagon on the bottom shaded green. From a point above the hexagon extend 6 segments, each connected to a vertex of the hexagon.

used in:

A cone is a three-dimensional figure like a pyramid, but the 1 base is a circle.

From an earlier course.

A cross-section is the new face that is seen when a three-dimensional figure is sliced.

A rectangular pyramid is sliced parallel to the base. The cross-section is a smaller rectangle.

<p>A plane cuts the pyramid parallel to the base.</p>

used in:

A cylinder is a three-dimensional figure like a prism, but with 2 bases that are circles.

From an earlier course.

A dependent variable represents the output of a function.

For example, someone needs to buy 20 pieces of fruit and decides to buy apples and bananas. If they select the number of apples first, the equation \(b=20-a\) shows the number of bananas they can buy. The number of bananas is the dependent variable because it depends on the number of apples.

used in:

A function is a rule that has exactly 1 output for each possible input.

In the function \(y=6x+4\), \(x\) is the input and \(y\) is the output. When \(x\) is 5, \(y\) has one value, 34.

\(\begin{align} y&=6x+4\\ y&=6(5)+4 \\ y&=34 \\ \end{align} \)

used in:

An independent variable represents the input of a function.

For example, suppose someone needs to buy 20 pieces of fruit and decides to buy some apples and bananas. If they select the number of apples first, the equation \(b=20-a\) shows the number of bananas they can buy. The number of apples is the independent variable because any number can be chosen for it.

used in:

A prism is a type of polyhedron with 2 bases that are identical and parallel. The bases are connected by parallelograms.

Here are some drawings of prisms.

A triangular prism. — triangular prism

A pentagonal prism. — pentagonal prism

A rectangular prism. — rectangular prism

used in:

A pyramid is a type of polyhedron that has 1 base. All the other faces are triangles that meet at a single vertex.

Here are some drawings of pyramids.

A rectangular pyramid. — rectangular pyramid

A hexagonal pyramid. — hexagonal pyramid

A heptagonal pyramid. — heptagonal pyramid

used in:

A radius is a line segment that goes from the center of a circle to any point on the circle. The length of this segment is also called the radius. Every radius of a circle is the same length.

For example, \(r\) is the radius of this circle with center \(O\).

<p>a circle with a labeled radius</p>

From an earlier course.

A sphere is a three-dimensional figure where any cross-section is a circle.

From an earlier course.

The surface area of a polyhedron is the number of square units that covers all of its faces with no gaps or overlaps.

For example, the 6 faces of a cube each have an area of 9 cm². So, the surface area of the cube is \(6 \boldcdot 9\), or 54 cm².

used in:

Volume is the number of cubic units that fill a three-dimensional region with no gaps or overlaps.

This rectangular prism has 3 layers that are each 20 units³. So, the volume of the prism is 60 units³.

Two images. First, a prism made of cubes stacked 5 wide, 4 deep, 3 tall. Second, each of the layers of the prism is separated to show 3 prisms 5 wide, 4 deep, 1 tall.

used in:

Unit 6 Resources

Student Materials