Common Core: 7.G.3 Suggested Learning Targets
What is a cross section? The following diagrams show the horizontal and vertical slices of a rectangular prism. Scroll down the page for examples and solutions.  How to describe the cross sections of a right rectangular prism by slicing at different angles? Example: A chef needs a piece of cheese for a new recipe. The chef makes a straight top to bottom slice from a block of cheese. How are the attributes of the piece of cheese and the attributes of the block of cheese alike? How are they different? Explain your reasoning. A cross section is the intersection of a three-dimensional figure and a plane. You can think of a cross section as a two-dimensional slice of the figure. A vertical slice can be parallel to the left and right faces. The cross section always has the same shape and dimensions as there faces. A vertical slice can also be parallel to the front and back faces. The cross section always has the same shape and dimensions as these faces. A horizontal slice is parallel to the bases. The cross section always has the same shape and dimensions as these faces. How to draw cross sections? Examples:
The following diagrams show the horizontal and vertical slices of a rectangular pyramid. Scroll down the page for examples and solutions. How to describe the cross sections of a right rectangular pyramid by slicing at different angles? Example: A waiter slices his restaurant’s world-famous meatloaf as shown for two diners to share. Could the waiter’s split be even? Is there a better way to make sure? Explain. If you make any horizontal slice of a rectangular pyramid, the resulting cross section, or slice, is a rectangle. The size of the rectangle depends on the distance of the slice from the base. If you make a vertical slice of a rectangular pyramid through the vertex, the resulting cross
section, or slice, is an isosceles triangle. The base of the triangle is equal in length to an
edge of the triangular base. The height of the triangle is equal to the height of the pyramid.
Examples:
Nets and Cross Sections of Solids Example:
Slicing 3-D Figures A cross section is the two-dimensional shape that results from cutting a three-dimensional with a plane. How to identify the face shape from cuts made parallel and perpendicular to the bases of right dimensional figures? Parallel cuts will take the shape of the base. Perpendicular cuts will take the shape of the lateral face. Cuts made at an angle through the right rectangular prism or pyramid will produce a parallelogram.
Cross Sections of 3 Dimensional Figures Example: The fruit to the right has been slice horizontally. Since the fruit represented is usually a sphere, the resulting cross section is a circle. Horizontal slice, vertical slice and angled slice of a rectangular pyramid. Horizontal slice, vertical slice and angled slice of a cylinder.
What is the shape of the cross section?
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What are the shapes of the cross sections formed by a plane slicing the rectangular pyramid?
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