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Boss lesson · The Grain Silo
Exam-hall rules, harvest week
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Exam-hall rules, harvest week

This is the boss. No calculator — and π\pi, the number that never ends, stays a SYMBOL: every line's answer is a clean number times π, so carry the coefficient and let π ride. Only the very last line turns π into a number, and today it rounds all the way to 3 — the exam-hall estimate, close enough to size a paint order. One silo: a cylinder wearing a half-sphere dome. Fill it, then paint it — and every answer feeds the next, so write each line down. One early slip pours all the way down the silo.

Everything from the chapter rides along: the cylinder, the hemisphere, the wall, the dome's curve. 5★ under par here is the chapter crown. Ladder up.

rhV

V=πr2hV = \pi r^{2} h

  • VV= Volume (volume)
  • rr= Radius (length)
  • hh= Height (length)
Cylinder Volume solver →
rV

V=23πr3V = \frac{2}{3}\pi r^3

  • VV= Volume (volume)
  • rr= Radius (length)
Hemisphere Volume solver →
rhA

A=2πrhA = 2\pi r h

  • AA= Lateral surface area (area)
  • rr= Radius (length)
  • hh= Height (length)
Cylinder Lateral Surface Area solver →
rA

A=3πr2A = 3\pi r^2

  • AA= Total surface area (area)
  • rr= Radius (length)
Hemisphere Total Surface Area solver →
no calculator in the boss room — the numbers are chosen to fit in your head