**Base:**The top and bottom circular faces of a cylinder.**Height:**The distance between the two bases of the cylinder.**Radius (r):**The distance from the center of the base to the edge of the base.**Diameter (d):**The distance across the center of the base, passing through the radius.**Surface Area:**The total area of all the surfaces of the cylinder, including the bases and the curved surface.**Volume:**The amount of space inside the cylinder.

**Surface Area (A):**A = 2πr^{2}+ 2πrh**Volume (V):**V = πr^{2}h

- Surface Area: A = 2π(4)
^{2}+ 2π(4)(6) = 32π + 48π = 80π ≈ 251.2 cm^{2} - Volume: V = π(4)
^{2}(6) = 16π(6) = 96π ≈ 301.6 cm^{3}

- Understand the concept of a cylinder and be able to identify its key components (bases, height, radius).
- Practice using the formulas for surface area and volume, and understand how to apply them in different scenarios.
- Work on problems that involve real-world applications of cylinders, such as calculating the volume of a cylindrical container or the surface area of a cylinder-shaped object.
- Review the relationship between the radius, diameter, and height of a cylinder, and how changes in these measurements affect the surface area and volume.

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.