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7th grade · Math · Unit 19 of 20

Slicing Solids

What shape is the cut?

What your child practices

Picturing the flat shape you get when you slice a prism, pyramid, cylinder, cone or sphere parallel or perpendicular to its base, like slicing a loaf of bread or a block of cheese.

New York State Learning Standards learning standard: NY-7.G.3 · describing the two-dimensional shapes made by slicing three-dimensional solids parallel or perpendicular to the base

How we explain it

Children can open this short lesson before they practice.

  1. A slice parallel to the base of a prism or cylinder is the same shape and size as the base.
  2. Slices of a pyramid or cone parallel to the base keep the base's shape but get smaller toward the top.
  3. A slice straight down through a cylinder is a rectangle; through the tip of a cone or pyramid, a triangle.

Example: A cylinder is sliced parallel to its base. What shape is the slice? The base of a cylinder is a circle. A slice parallel to the base matches it. Answer: A circle the size of the base

Slicing Solids in New York

In the New York State Learning Standards, this is unit 19 of 20 in 7th grade Math, after One Triangle, Many or None? and before Area of Composite Shapes.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: New York State Education Department (NYSED)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A cube is sliced parallel to one face. What shape is the slice?

    • a square
    • a triangle
    • a hexagon
    • a circle

  2. Question 2

    As you slice a prism parallel to its base, moving up, the slices…

    • get smaller
    • stay the same shape and size
    • turn into triangles
    • get bigger

  3. Question 3

    A square pyramid is sliced straight down through its top point. What shape is the slice?

    • a circle
    • a square
    • a triangle
    • a rectangle

  4. Question 4

    A box is 3 cm long, 8 cm wide and 5 cm tall. It is sliced straight down, parallel to its 3 cm by 5 cm front face. What is the area of the slice, in cm²?

    • 40
    • 24
    • 120
    • 15

  5. Question 5

    A cone is sliced parallel to its base. What shape is the slice?

    • a circle bigger than the base
    • a triangle
    • a rectangle
    • a circle smaller than the base

  6. Question 6

    A box is 12 cm long, 4 cm wide and 3 cm tall. It is sliced straight down, parallel to its 12 cm by 3 cm front face. What is the area of the slice, in cm²?

    • 48
    • 12
    • 144
    • 36

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