Unit · Measurement
Capacity & Volume
20 carefully crafted questions — from basic units to tricky word problems. Work through each at your own pace.
Quick Memory Points — memorize these first!
VOLUME= l × w × h (space inside)
CAPACITY= how much liquid it holds
1 L= 1,000 mL
1 cm³= 1 mL
1 m³= 1,000 L
KILO-× 1,000 bigger
MILLI-÷ 1,000 smaller
CUBEV = s³ (all sides equal)
📐 Formula Reference Card
Rectangular Prism Volume
V = l × w × h
Cube Volume
V = s³
Cylinder Volume
V = π × r² × h
Liquid Conversion
1 L = 1,000 mL
Volume ↔ Capacity
1 cm³ = 1 mL
Large Volume
1 m³ = 1,000 L
Section 1 · Basic Units & Conversions
How many milliliters (mL) are in 1 liter (L)?
💡 Think about the prefix "milli-" — it always means one-thousandth.
🔑 Key Word MILLI = 1/1,000 → so 1 L = 1,000 mL, 1 m = 1,000 mm
Convert 3.5 L to milliliters.
3.5 L = ? mL
Remember: to convert liters → mL, multiply by 1,000.
🔑 Trick L → mL: move decimal point 3 places RIGHT (× 1,000)
Convert 2,400 mL to liters.
2,400 mL = ? L
Careful! This is the reverse — dividing, not multiplying.
🔑 Trick mL → L: move decimal point 3 places LEFT (÷ 1,000)
What is the volume of this rectangular box?
📦 Length = 5 cm, Width = 4 cm, Height = 3 cm
V = l × w × h = 5 × 4 × 3 = ?
🔑 Formula V = l × w × h — always in cubic units (cm³)
A cube has sides of 4 cm. What is its volume?
V = s³ = 4³ = 4 × 4 × 4 = ?
A cube is a special box where all three sides are the same length.
🔑 Cube V = s³ means side × side × side (NOT side × 3!)
Section 2 · Volume ↔ Capacity Connection
A container has a volume of 500 cm³. How many mL of water can it hold?
This is the KEY relationship: 1 cm³ = 1 mL exactly!
500 cm³ = ? mL
🔑 Magic Link 1 cm³ = 1 mL — volume and capacity share this bridge!
A fish tank measures 30 cm × 20 cm × 25 cm. What is its capacity in liters?
Step 1: V = 30 × 20 × 25 = 15,000 cm³
Step 2: 15,000 cm³ = 15,000 mL = ? L
Step 2: 15,000 cm³ = 15,000 mL = ? L
🔑 Two-Step cm³ → mL (same number!) → ÷ 1,000 → L
Which container holds MORE water?
Container A: 8 cm × 6 cm × 5 cm
Container B: 10 cm × 4 cm × 6 cm
Container B: 10 cm × 4 cm × 6 cm
⚠️ Common mistake: students pick the bigger-looking shape without calculating!
🔑 Always Calculate A = 240 cm³, B = 240 cm³ — shape looks different but volume can be equal!
Convert 2 m³ to liters.
1 m³ = 1,000 L → 2 m³ = ? L
This is a different conversion: cubic meters to liters!
🔑 Big Units 1 m³ = 1,000 L (not 1 mL!) — don't mix up m³ and cm³
A bottle contains 750 mL of juice. Sarah drinks 0.25 L. How much juice is left?
⚠️ Mixed units! You must convert before subtracting.
0.25 L = 250 mL → 750 - 250 = ? mL
🔑 Rule SAME UNITS before you add or subtract! Always convert first.
Section 3 · Word Problems & Applications
A swimming pool is 10 m long, 5 m wide and 2 m deep. What is the volume of water needed to fill it?
V = l × w × h = 10 × 5 × 2 = ? m³
🔑 Same Formula V = l × w × h works for ALL rectangular prisms, big or small!
If you double ALL three dimensions of a box, how many times bigger does the volume become?
Original: 2 × 3 × 4 = 24 cm³
Doubled: 4 × 6 × 8 = ?
Doubled: 4 × 6 × 8 = ?
⚠️ Most students say "2 times bigger" — but that's WRONG!
🔑 Scale Rule Double all sides → 2³ = 8× bigger! Volume scales by the CUBE of the scale factor.
A recipe needs 1.5 L of milk. You only have a 250 mL cup. How many cups do you need?
1.5 L = 1,500 mL → 1,500 ÷ 250 = ?
🔑 Two-Step Always convert to the SAME unit FIRST, then divide.
A box is 10 cm × 10 cm × 10 cm. It is filled with water. How many liters does it hold?
V = 10³ = 1,000 cm³ → 1,000 mL = ? L
⚠️ Many students stop at cm³ and forget to convert to liters!
🔑 Classic 1,000 cm³ = 1,000 mL = 1 L — this exact relationship is worth memorizing!
A tank holds 4,000 mL and is currently ¼ full. How much more water (in L) is needed to fill it?
¼ full = 4,000 ÷ 4 = 1,000 mL already in
Need: 4,000 − 1,000 = 3,000 mL = ? L
Need: 4,000 − 1,000 = 3,000 mL = ? L
🔑 Fraction Check ¾ of the tank is EMPTY → ¾ × 4,000 mL = 3,000 mL = 3 L
Section 4 · Challenge Questions
A stone is dropped into a rectangular tank (10 cm × 5 cm). The water level rises by 2 cm. What is the volume of the stone?
Volume of stone = base area × rise in water
= (10 × 5) × 2 = ?
= (10 × 5) × 2 = ?
⚠️ This is displacement! The stone pushes water up by its own volume.
🔑 Displacement Object volume = Tank base area × water level rise. Archimedes discovered this!
A jug holds 2 L. You pour 3 full jugs and 500 mL extra into a bucket. How many mL are in the bucket?
3 × 2,000 mL + 500 mL = ?
🔑 Convert First 2 L = 2,000 mL → then multiply → then add the extra 500 mL
Which measurement is LARGEST?
(A) 5,200 mL | (B) 5.02 L | (C) 5,020 mL | (D) 0.052 kL
⚠️ Convert all to mL to compare. Watch out for kL (kiloliter = 1,000 L)!
🔑 kL Hidden 1 kL = 1,000 L → 0.052 kL = 52 L = 52,000 mL — 10× bigger than the others!
A rectangular box is 6 cm × 4 cm × h cm. Its volume is 120 cm³. Find the height h.
120 = 6 × 4 × h → 120 = 24h → h = ?
🔑 Reverse Formula h = Volume ÷ (l × w) = 120 ÷ 24 = 5
A cylindrical glass has a radius of 3 cm and height 10 cm. Approximately how much water does it hold? (Use π ≈ 3.14)
V = π × r² × h = 3.14 × 3² × 10 = 3.14 × 9 × 10 = ?
This is a cylinder — a round container! Different formula from a box.
🔑 Cylinder V = π × r² × h → cm³ = mL (same bridge as always!)
Quiz Complete!
—
questions correct