- Comprehend that surface area and volume are two different attributes of three-dimensional objects and are measured in different units.
- Estimate measurements of a prism in a real-world situation, and explain (orally) the estimation strategy.
- Interpret different methods for calculating the surface area of a prism, and evaluate (orally and in writing) their usefulness.
Assemble the net from the blackline master to make a prism with a base in the shape of a plus sign. Make sure to print the blackline master at 100% scale so the dimensions are accurate. This prism will be used for both the warm-up and the following activity.
- I can find and use shortcuts when calculating the surface area of a prism.
- I can picture the net of a prism to help me calculate its surface area.
base (of a prism or pyramid)
The word base can also refer to a face of a polyhedron.
A prism has two identical bases that are parallel. A pyramid has one base.
A prism or pyramid is named for the shape of its base.
A cone is a three-dimensional figure like a pyramid, but the base is a circle.
A cross section is the new face you see when you slice through a three-dimensional figure.
For example, if you slice a rectangular pyramid parallel to the base, you get a smaller rectangle as the cross section.
A cylinder is a three-dimensional figure like a prism, but with bases that are circles.
A prism is a type of polyhedron that has two bases that are identical copies of each other. The bases are connected by rectangles or parallelograms.
Here are some drawings of prisms.
A pyramid is a type of polyhedron that has one base. All the other faces are triangles, and they all meet at a single vertex.
Here are some drawings of pyramids.
A sphere is a three-dimensional figure in which all cross-sections in every direction are circles.
The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps.
For example, if the faces of a cube each have an area of 9 cm2, then the surface area of the cube is \(6 \boldcdot 9\), or 54 cm2.
Volume is the number of cubic units that fill a three-dimensional region, without any gaps or overlaps.
For example, the volume of this rectangular prism is 60 units3, because it is composed of 3 layers that are each 20 units3.
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