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Volume of cylinders and pyramids

A 20-item reviewer. Read the formula notes first, then answer each question. After you choose, the full solution appears so you can check your steps. Use π = 3.14 unless the answer is written with π.

Formula notes

r h

Cylinder

  1. A cylinder is a stack of identical circles, just like a prism is a stack of identical bases.
  2. Volume of any prism-like solid = Base area × height, or V = B × h.
  3. The base is a circle, so B = πr².
  4. Substitute: V = πr² × h.

V = πr²h

To find h: h = V ÷ (πr²). To find r: r = √(V ÷ (πh)).

h s

Square pyramid

  1. Take a prism and a pyramid with the same base and same height.
  2. Fill the pyramid with sand and pour it into the prism. It takes exactly 3 pyramids to fill the prism.
  3. So the pyramid is one-third of the prism: V = ⅓ × B × h.
  4. The base is a square, so B = s × s = s².

V = ⅓ s²h

To find h: h = 3V ÷ s². To find s: s = √(3V ÷ h).

h l w

Rectangular pyramid

  1. Same idea as the square pyramid: a pyramid is ⅓ of the prism with the same base and height.
  2. The base is a rectangle, so B = l × w.
  3. Substitute: V = ⅓ × (l × w) × h.

V = ⅓ lwh

To find h: h = 3V ÷ (lw). To find a missing side: l = 3V ÷ (wh).

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