Seventh Grade · Math · week 30

Volume and surface area of cylinders

Apply the volume formula V = pi x r^2 x h and the surface area formula for a right circular cylinder.

A cylinder is a stack of identical circles, so its volume builds directly on the circle-area formula: V = pi x r^2 x h, the circle's area multiplied by how tall the stack is.

Surface area means the total area of every surface: the two circular ends (each pi x r^2) plus the curved side, which unrolls into a rectangle with area 2 x pi x r x h. Add all three pieces together: SA = 2 x pi x r^2 + 2 x pi x r x h.

📋 For the teacher
Teach it (10–15 min):
  • Connect volume back to "circle area times height" -- it is the exact same stacking idea as area of a prism, just with a circular base.
  • For surface area, physically picture peeling a label off a can: it unrolls into a flat rectangle, which is exactly the curved-side piece of the formula.
  • Watch order of operations closely: square the radius FIRST, before multiplying by height or pi.
  • Keep the exact form (like 90 x pi) visible next to the decimal estimate throughout this week.
Talk about it:
  • Why does a cylinder's volume formula start with the circle-area formula?
  • What real object does the curved side of a cylinder become when you "unroll" it?
  • Why is the radius squared in both the volume and the end-circle parts of surface area?

Mastery looks like: They correctly compute the volume and surface area of a cylinder, keeping order of operations correct throughout.

Common stumbles: Multiplying the radius by other numbers before squaring it; forgetting one of the three surface-area pieces (either circular end, or the curved side).

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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