Topics
1. Surface Area
Key terms – you should be able to define and apply each key term
Edge, Face, Height, Nets
Formulas:
Surface area of a cylinder = 2𝜋𝑟 2 + 2𝜋𝑟ℎ ( r is the radius, h is the height of the cylinder)
Surface area of a prism = 2B + Ph; (B is the area of the base, P is the perimeter of the base, and h
is the height)
Learning Targets:
1. Calculate the surface area of cylinders and prisms. (MS 7.3.1.2)
2. Be able to justify the formulas used in calculating the surface area of cylinders and prisms.
(MS 7.3.1.2)
3. Develop nets to calculate surface areas of cylinders and prisms.
4. Be able to use surface area to solve real-world situations.
2. Volume
Key Terms – you should be able to define and apply each key term
Base, Cube, Cone, Cylinder, Prism, Height, Sphere, Unit Cube
Formulas:
Volume of a cylinder = 𝜋𝑟 2 ℎ
Volume of a prism = (B)h; where B is the area of the base and h is the height of the prism
4
Volume of a sphere = 3 𝜋𝑟 3
1
Volume of a cone = 3 𝜋𝑟 2 h
Learning Targets:
1. Calculate the volume of cylinders, prisms, spheres, and cones. (MS 7.3.1.2)
2. Be able to justify the formulas used in calculating the volume of cylinders, prisms, and
spheres. (MS 7.3.1.2)
3. Be able to use volume to solve real-world situations
3. Circles
Key Terms –you should be able to define and apply each key term
Sector, Pi or 𝜋
Formulas:
Area of a circle = 𝜋𝑟 2
Circumference of a circle = 2𝜋𝑟
Learning Targets:
1. Explain how the diameter and circumference of a circle is the unit rate called 𝜋 . (MS
7.3.1.1)
2. Calculate the circumference of circles and sectors of circles. (MS 7.3.1.1)
3. Calculate the area of circles and sectors of circles. (MS 7.3.1.1)
4 Mathematical Relationships
Key Terms – you should be able to define and apply all previous concepts
Learning Targets:
1. Be able to apply similarity and scale factors to three-dimensional figures. (MS 7.3.2.1)
2. Explain why three-dimensional figures may have the same volume but different surface
areas.
3. Explain how changes in one or more dimensions of a rectangular prism or cylinder affect
the prism’s volume.
4. Explain how changes in one or more dimensions of a rectangular prism or cylinder affect
the prism’s surface area.
Vocabulary Developed in Previous Units
area radius
circumference
congruent
height
length
perimeter
pi (𝜋)
right prism
oblique prism
width
Vocabulary Developed in this Unit
Base The face of a three-dimensional
chosen to be the “bottom” face.
Cone A three-dimensional shape with a circular base
opposite the base.
Cube A three-
shape
and a vertex
dimensional shape with six identical square faces.
Cylinder A three-dimensional shape with two opposite
are congruent circles. The side (lateral surface) is a
that is “wrapped around” the circular faces at the ends.
Edge A line segment formed where two faces of a threedimensional shape meet.
Face A flat two-dimensional surface of a three-dimensional shape.
faces that
rectangle
Height The vertical distance between the face
chosen to be the base and
• the opposite face of a prism or cylinder, or
• the vertex of a cone or pyramid.
Net A two-dimensional pattern that can be folded into a three-dimensional figure.
Oblique prism A prism whose side faces are non-rectangular
parallelograms.
Prism A three-dimensional shape with a top and bottom (base) that are
congruent polygons and lateral faces that are parallelograms.
Rectangular prism A prism with a top and bottom (base) that are
congruent rectangles.
Pyramid A three-dimensional shape with one polygonal base and
lateral sides are all triangles that meet at a vertex opposite the base.
Sphere A three-dimensional shape whose surface consists of all the points that are a given distance
from the center of the shape.
Surface area The area required to cover a three-dimensional shape.
Unit cube A cube whose edges are 1 unit long. It is the basic unit of measurement for volume.
Volume The amount of space occupied by, or the capacity of, a three-dimensional shape. The
volume is the number of unit cubes that will fit into a three-dimensional shape.