Estimate how many scoops of ice cream can be obtained from a cuboidal container of dimensions 10 cm × 15 cm × 20 cm.
Answer: Container = 3000 cm3. A scoop is roughly a ball of diameter 5 cm, about 65 cm3. 3000 ÷ 65 ≈ 46, so about 45 scoops.
Step-by-step solution
Idea: Number of scoops ≈ volume of ice cream ÷ volume of one scoop. Model a scoop as a sphere of a sensible size.
- Guess first: perhaps about 50 scoops.½ mark
- Volume of ice cream = 10 × 15 × 20 = 3000 cm3 (assuming the container is full).½ mark
- Assume a scoop is a sphere of diameter about 5 cm (r = 2.5 cm): volume = 43 × 3.14 × 2.53 ≈ 65.4 cm3.1 mark
- Number of scoops ≈ 3000 ÷ 65.4 ≈ 46. So about 45 scoops, close to the guess. (Bigger 6 cm scoops of about 113 cm3 would give about 26.)1 mark
About 45 scoops (container 3000 cm³, scoop about 65 cm³).
Check: A family tub of 3 litres is usually said to serve 40–50 scoops, which matches ✓.
Answer to write in the exam
Volume of container = 10 × 15 × 20 = 3000 cm3
Scoop ≈ sphere, r = 2.5 cm: V = 43 × 3.14 × 2.53 ≈ 65.4 cm3
Number = 3000 ÷ 65.4 ≈ 46
∴ About 45 scoops
Common mistakes that cost marks
- Using the diameter as the radius, which makes each scoop 8 times too large.
- Giving an exact answer with no assumption stated; a guesstimate must say what was assumed.
How this can come in the exam
Short answer (2 marks)
A cylindrical tub of radius 7 cm and height 12 cm is full of ice cream. How many hemispherical scoops of radius 3.5 cm can be served? (π = 227)
Show answer
Tub = 227 × 49 × 12 = 1848 cm3. Scoop = 23 × 227 × 42.875 ≈ 89.83 cm3. 1848 ÷ 89.83 ≈ 20.6, so 20 scoops.Try one yourself
Estimate the number of 2 cm sugar cubes needed to fill a box 10 cm × 8 cm × 6 cm.
Show answer
5 × 4 × 3 = 60 cubes.
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