NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
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Volume and capacity of prisms

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A rectangular prism-shaped storage unit in Sydney has internal dimensions of 61 cm in length, 36 cm in width, and 36 cm in height. The unit is to be filled with identical cylindrical containers, each with a volume of 1.44 litres.

What is the exact number of cylindrical containers that can fit inside the storage unit, assuming no space is wasted between containers? (Note: 1 litre = 1000 cm^3)

Concept illustrations

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A rectangular prism. A prism of length 4 cm, width 3 cm and height 2 cm has volume 24 cm³ = 24 mL. The perspective drawing is schematic.4 cm3 cm2 cm
A prism of length 4 cm, width 3 cm and height 2 cm has volume 24 cm³ = 24 mL. The perspective drawing is schematic.
Square the length conversion factor. A 1 m by 1 m square is 100 cm by 100 cm. Its area is 10,000 cm². The 10-by-10 grid shows 100 squares, each 10 cm by 10 cm.1 m = 100 cm1 m100 cm
A 1 m by 1 m square is 100 cm by 100 cm. Its area is 10,000 cm². The 10-by-10 grid shows 100 squares, each 10 cm by 10 cm.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The storage unit is a rectangular prism with internal dimensions: length = 61 cm, width = 36 cm, height = 36 cm. The volume of a rectangular prism is calculated as length × width × height.
  2. Substitute the given dimensions into the volume formula: V = 61 cm × 36 cm × 36 cm.
  3. First, compute 36 × 36 = 1296 cm².
  4. Now compute 61 × 1296. Break it down: 60 × 1296 = 77,760 and 1 × 1296 = 1296. Add: 77,760 + 1296 = 79,056 cm³.
  5. The volume of the storage unit is 79,056 cm³.
  6. Each cylindrical container has a volume of 1.44 litres. Convert litres to cm³ using the given conversion: 1 litre = 1000 cm³. So, 1.44 litres = 1.44 × 1000 = 1440 cm³.
  7. To find how many containers fit, divide the total volume of the storage unit by the volume of one container: 79,056 cm³ ÷ 1440 cm³ per container.
  8. Perform the division: 79,056 ÷ 1440. First, simplify the fraction: divide numerator and denominator by 24. 79,056 ÷ 24 = 3294, 1440 ÷ 24 = 60. So, 3294 ÷ 60.
  9. Now divide 3294 by 60: 60 × 54 = 3240, 3294 − 3240 = 54. So, 54 + 54/60 = 54.9. But we need the exact integer count of containers that fit without waste.
  10. Check if 1440 × 54 = 77,760. 1440 × 50 = 72,000; 1440 × 4 = 5760; total = 72,000 + 5760 = 77,760 cm³.
  11. Subtract from total volume: 79,056 − 77,760 = 1,296 cm³ remaining. This is less than 1440 cm³, so one more container cannot fit. Therefore, only 54 containers fit exactly.
  12. The maximum number of cylindrical containers that can fit without wasted space is 54. This assumes perfect packing with no gaps, as stated.

Reference answer: 54

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