Mathslive.ie

VOLUME & SA

Exam Cog
①THE BOX (CUBOID)

V = ℓ × b × h

A = 2(ℓb + bh + ℓh)

Open-top? drop one ℓb face.

②THE CYLINDER

V = πr²h

Curved = 2πrh

Closed total = 2πrh + 2πr²

★ Curved surface = a rolled-up rectangle 2πr by h
③THE SPHERE

V = (4/3)πr³

A = 4πr²

Set only by the radius r.

④THE CONE

V = (1/3)πr²h

A third of the matching cylinder.

Curved surface = πrl  (l = slant)

⑤UNITS & π

Length cm   Area cm²   Volume cm³

Leave answers in terms of π unless told π = 22/7 or 3.14.

⚠ WATCH: never mix units — convert first (1 m = 100 cm).
⑥WORKING BACKWARDS
  1. Write the right formula
  2. Put the given V or A in
  3. Solve for the missing length

e.g. πr²h = V → r² = V/(πh)

⑦‘SPACE’ / COMPOSITE

Space = volume left over.

Space = container − solid inside

Percentage empty = (space / container) × 100

★ Sphere in a cube: side = diameter = 2r
⑧READ THE SOLID

Solid = all faces   Open = one face missing

“Hollow / tube” → no ends

⑨EXAM METHOD
  1. Sketch & label the solid
  2. List what you know
  3. Pick the formula (all are in tables)
  4. State units
⑩KEY VOCAB

Radius centre→edge   Diameter = 2r

Capacity = volume it holds (1 litre = 1000 cm³)