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CHAPTER 5 MEASUREMENT

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**Ratios and Units of Measure**

SECTION 5-1 Ratios and Units of Measure

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**MEASUREMENT– is a process used to find size, quantities, or amounts**

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**COMPASS – is used for drawing curved lines and circles for measuring distances.**

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**PROTRACTOR – is an instrument for measuring and drawing angles.**

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**SCALES or RULERS – devices for measuring distance.**

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**CALIPERS and MICROMETERS – devices used for making precise measurements**

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**PRECISION – is related to the unit of measure used.**

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**GREATEST POSSIBLE ERROR – is ½ the smallest unit used to make the measurement.**

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**RATIO – is a quotient of two numbers that compares one number with the other.**

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**RATE – is a ratio that compares two different quantities**

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**UNIT RATE – compares a quantity to one unit of that quantity**

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**Perimeter, Circumference and Area**

SECTION 5-2 Perimeter, Circumference and Area

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**PERIMETER – is the distance around a polygon.**

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**CIRCUMFERENCE – is the distance around a circle.**

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**AREA – the amount of surface a figure covers.**

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Circle C = d or 2r A =r2

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Rectangle or Square P = 2l + 2w A = lw

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Triangle A = ½bh

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Parallelogram A = bh

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Trapezoid A = ½h(b1+b2)

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SECTION 5-3 Probability and Area

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**PROBABILITY – the likelihood that an event will occur.**

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**number of favorable outcomes ÷ number of possible outcomes**

P(any event) = number of favorable outcomes ÷ number of possible outcomes

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**Problem Solving Skills: Irregular Shapes**

SECTION 5-4 Problem Solving Skills: Irregular Shapes

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**Three-dimensional Figures and Loci**

SECTION 5-5 Three-dimensional Figures and Loci

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**POLYHEDRON– is a three-dimensional figure in which each surface is a polygon and**

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**The surfaces are called faces**

The surfaces are called faces. Two faces intersect at an edge, and a vertex is a point where three or more edges intersect.

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**PRISM - a polyhedron with two identical parallel faces**

PRISM - a polyhedron with two identical parallel faces. Each of these faces is called a base and

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**a prism is named by the shape of its bases.**

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**PYRAMID - a polyhedron with only one base**

PYRAMID - a polyhedron with only one base. The other faces are triangles that meet at a vertex and

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**a pyramid is named by the shape of its base.**

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**LATERAL FACES - are those faces that are not bases.**

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**LATERAL EDGES - are the edges of lateral faces and can be parallel, intersecting,or skew.**

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CYLINDER - a three-dimensional figure having a curved region with two parallel congruent circular bases. Its axis joins the centers of the two bases.

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CONE - a three-dimensional figure having a curved surface and one circular base. Its axis is a segment from the vertex to the center of the base.

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SPHERE - is the set of points in space that are the same distance from a given point called the center of the sphere.

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**Surface Area of Three-dimensional Figures**

SECTION 5-6 Surface Area of Three-dimensional Figures

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**SURFACE AREA - The sum of the areas of all the faces of a three-dimensional figure.**

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FORMULAS

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Square base A = s2

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Square prism SA = 6s2

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Rectangular Prism SA = 2(lw + lh + wh)

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Triangular face A = ½bh

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Circular base A = r2

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Curved surface A = 2rh

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Cylinder SA = 2rh + 2r2

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Cone SA = rs + r2 S is the slant height

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Sphere SA = 4r2

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**Volume of Three-dimensional Figures**

SECTION 5-7 Volume of Three-dimensional Figures

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FORMULAS

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**where B = area of the given base**

Prism V = Bh where B = area of the given base

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**where B = area of the given base**

Pyramid V = 1/3Bh where B = area of the given base

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Cylinder V = r2h

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Cone V = 1/3r2h

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Sphere V = 4/3r3

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END

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