SOL Objective(s):
7.5 The student will...
a) describe volume and surface area of cylinders;
b) solve practical problems involving the volume and surface area of rectangular prisms and cylinders; and
c) describe how changing one measured attribute of a rectangular prism affects its volume and surface area.
8.7 The student will
a) investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids; and
b) describe how changing one measured attribute of the figure affects the volume and surface area.
a) describe volume and surface area of cylinders;
b) solve practical problems involving the volume and surface area of rectangular prisms and cylinders; and
c) describe how changing one measured attribute of a rectangular prism affects its volume and surface area.
8.7 The student will
a) investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones, and pyramids; and
b) describe how changing one measured attribute of the figure affects the volume and surface area.
Previous/Related SOL Objectives:6.10 The student will
a) define π (pi) as the ratio of the circumference of a circle to its diameter; b) solve practical problems involving circumference and area of a circle, given the diameter or radius; c) solve practical problems involving area and perimeter; and d) describe and determine the volume and surface area of a rectangular prism. 
Prerequisite Skills:
Know the difference between volume and surface area.
Know the names of various 3dimensional shapes Know the difference between perimeter and area 
Khan Skill Phrases:

The Basics and Background Information
• The area of a rectangle is computed by multiplying the lengths of two adjacent sides.
• The area of a circle is computed by squaring the radius and multiplying that product by π (A = πr2 , where π ≈3.14 or 22/7 ).
•A rectangular prism can be represented on a flat surface as a net that contains six rectangles —two that have measures of the length and width of the base, two others that have measures of the length and height, and two others that have measures of the width and height. The surface area of a rectangular prism is the sum of the areas of all six faces ( SA = 2lw+ 2lh + 2wh ).
•A cylinder can be represented on a flat surface as a net that contains two circles (bases for the cylinder) and one rectangular region whose length is the circumference of the circular base and whose width is the height of the cylinder. The surface area of the cylinder is the area of the two circles and the rectangle (SA = 2πr2 + 2πrh).
•The volume of a rectangular prism is computed by multiplying the area of the base, B, (length times width) by the height of the prism (V = lwh = Bh).
•The volume of a cylinder is computed by multiplying the area of the base, B, (πr2) by the height of the cylinder (V = πr2h = Bh).
• There is a direct relationship between changing one measured attribute of a rectangular prism by a scale factor and its volume. For example, doubling the length of a prism will double its volume. This direct relationship does not hold true for surface area.
• A polyhedron is a solid figure whose faces are all polygons.
• A pyramid is a polyhedron with a base that is a polygon and other faces that are triangles with a common vertex.
• The area of the base of a pyramid is the area of the polygon which is the base.
• The total surface area of a pyramid is the sum of the areas of the triangular faces and the area of the base.
• The volume of a pyramid is 13 Bh, where B is the area of the base and h is the height.
• The area of the base of a circular cone is πr2.
•The surface area of a right circular cone is πr2 + πrl, here l represents the slant height of the cone.
•The volume of a cone is 13 πr2h, where h is the height and πr2 is the area of the base.
•The surface area of a right circular cylinder is 2π r2 + 2π rh .
•The volume of a cylinder is the area of the base of the cylinder multiplied by the height.
•The surface area of a rectangular prism is the sum of the areas of the six faces.
•The volume of a rectangular prism is calculated by multiplying the length, width and height of the prism.
• A prism is a solid figure that has a congruent pair of parallel bases and faces that are parallelograms. The surface area of a prism is the sum of the areas of the
faces and bases.
• When one attribute of a prism is changed through multiplication or division the volume increases by the same factor that the attribute increased by. For example, if a prism has a volume of 2 x 3 x 4, the volume is 24. However, if one of the attributes are doubled, the volume doubles.
• The volume of a prism is Bh, where B is the area of the base and h is the height of the prism.
• Nets are twodimensional representations that can be folded into threedimensional figures.
• The area of a circle is computed by squaring the radius and multiplying that product by π (A = πr2 , where π ≈3.14 or 22/7 ).
•A rectangular prism can be represented on a flat surface as a net that contains six rectangles —two that have measures of the length and width of the base, two others that have measures of the length and height, and two others that have measures of the width and height. The surface area of a rectangular prism is the sum of the areas of all six faces ( SA = 2lw+ 2lh + 2wh ).
•A cylinder can be represented on a flat surface as a net that contains two circles (bases for the cylinder) and one rectangular region whose length is the circumference of the circular base and whose width is the height of the cylinder. The surface area of the cylinder is the area of the two circles and the rectangle (SA = 2πr2 + 2πrh).
•The volume of a rectangular prism is computed by multiplying the area of the base, B, (length times width) by the height of the prism (V = lwh = Bh).
•The volume of a cylinder is computed by multiplying the area of the base, B, (πr2) by the height of the cylinder (V = πr2h = Bh).
• There is a direct relationship between changing one measured attribute of a rectangular prism by a scale factor and its volume. For example, doubling the length of a prism will double its volume. This direct relationship does not hold true for surface area.
• A polyhedron is a solid figure whose faces are all polygons.
• A pyramid is a polyhedron with a base that is a polygon and other faces that are triangles with a common vertex.
• The area of the base of a pyramid is the area of the polygon which is the base.
• The total surface area of a pyramid is the sum of the areas of the triangular faces and the area of the base.
• The volume of a pyramid is 13 Bh, where B is the area of the base and h is the height.
• The area of the base of a circular cone is πr2.
•The surface area of a right circular cone is πr2 + πrl, here l represents the slant height of the cone.
•The volume of a cone is 13 πr2h, where h is the height and πr2 is the area of the base.
•The surface area of a right circular cylinder is 2π r2 + 2π rh .
•The volume of a cylinder is the area of the base of the cylinder multiplied by the height.
•The surface area of a rectangular prism is the sum of the areas of the six faces.
•The volume of a rectangular prism is calculated by multiplying the length, width and height of the prism.
• A prism is a solid figure that has a congruent pair of parallel bases and faces that are parallelograms. The surface area of a prism is the sum of the areas of the
faces and bases.
• When one attribute of a prism is changed through multiplication or division the volume increases by the same factor that the attribute increased by. For example, if a prism has a volume of 2 x 3 x 4, the volume is 24. However, if one of the attributes are doubled, the volume doubles.
• The volume of a prism is Bh, where B is the area of the base and h is the height of the prism.
• Nets are twodimensional representations that can be folded into threedimensional figures.
Essential Knowledge and Skills
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to...
• Determine if a practical problem involving a rectangular prism or cylinder represents the application of volume or surface area.
• Find the surface area of a rectangular prism.
• Solve practical problems that require finding the surface area of a rectangular prism.
• Find the surface area of a cylinder.
• Solve practical problems that require finding the surface area of a cylinder.
• Find the volume of a rectangular prism.
• Solve practical problems that require finding the volume of a rectangular prism.
• Find the volume of a cylinder.
• Solve practical problems that require finding the volume of a cylinder.
• Describe how the volume of a rectangular prism is affected when one measured attribute is multiplied by a scale factor. Problems will be limited to
changing attributes by scale factors only.
• Describe how the surface area of a rectangular prism is affected when one measured attribute is multiplied by a scale factor. Problems will be
limited to changing attributes by scale factors only.
• Determine if a practical problem involving a rectangular prism or cylinder represents the application of volume or surface area.
• Find the surface area of a rectangular prism.
• Solve practical problems that require finding the surface area of a rectangular prism.
• Find the surface area of a cylinder.
• Solve practical problems that require finding the surface area of a cylinder.
• Find the volume of a rectangular prism.
• Solve practical problems that require finding the volume of a rectangular prism.
• Find the volume of a cylinder.
• Solve practical problems that require finding the volume of a cylinder.
• Describe how the volume of a rectangular prism is affected when one measured attribute is multiplied by a scale factor. Problems will be limited to
changing attributes by scale factors only.
• Describe how the surface area of a rectangular prism is affected when one measured attribute is multiplied by a scale factor. Problems will be
limited to changing attributes by scale factors only.
Vocabulary and Things to Know:Surface Area Formulas:
Cube: SA = 6 s^2 Rectangular Prism: SA = 2lw + 2lh + 2wh Cylinder: ANY prism (including cylinder): (perimeter of end shape) * (distance between end shapes) + 2(Area of end shape) Pyramid: SA = 1/2 lp + B Cone: SA = (pi)r^2 + (pi)rl Volume Formulas: Cube: V = lwh Rectangular Prism: V = lwh Cylinder: V = (pi)r^2h ANY prism (including cylinder): V = Bh Pyramid: V = 1/3 Bh Cone:V = 1/3 (pi)r^2h Variables in formulas: SA: Surface Area V: Volume s: side l: length l (on pyramid or cone): slant height w: width h: height (distance between two areas and perpendicular to base) r: radius (1/2 diameter) d: diameter (twice radius) p: perimeter B: area of base Formulas for parts of solids Pythagorean Theorem can be used to find missing measurements (NOW, this is a skill and tool to be used to find more measuerments.) 
Be Able To:Find surface area of cubes, rectangular prisms, cylinders, pyramids, and cones
Find volume of cubes, rectangluar prisms, cylinders, pyramids, and cones "Cut apart" formulas to find parts of solid measurements Apply skills for finding composite shapes to "composite" solids: both adding different parts, as well as subtracting parts. Present work in algebraically formatted equations. 
The topic: What is it and what will we learn?
Distinguish between surface area and volume and then find those measurements using appropriate formulas and/or parts of formulas.
So...
1. Identify what you're looking for  surface area or volume.
2. Identify the solids involved.
3. Choose an appropriate formula. (Revise the formula for parts, if needed.
4. Substitute known measurements.
5. Solve.
6. For "composite" solids, use skills learned with composite shapes. You can either add measurements together or you can subtract measurements, depending on the situation.
So...
1. Identify what you're looking for  surface area or volume.
2. Identify the solids involved.
3. Choose an appropriate formula. (Revise the formula for parts, if needed.
4. Substitute known measurements.
5. Solve.
6. For "composite" solids, use skills learned with composite shapes. You can either add measurements together or you can subtract measurements, depending on the situation.
ThreeDimensional SolidsA quick review of the names of various solids.


PrismsElaboration on definitions and properties of prisms.


Math.com: Surface Area FormulasFormulas and explanations of those formulas.

AAAMath.comIllustrations and explanations along with online practice of finding various surface area and volume.

Volume and Surface Area FormulasSolids are constructed to show volume formulas and then "peeled open" to show surface area formulas.


Practice Word Problems 
Thatquiz.orgSelect solids and find surface area and/or volume. The online quizzes will let you know if you're correct or not and time your progress.
