A closed rectangular container has the same base area from top to bottom. When it stands upright on its base, it holds 1350 cm³ of orange juice and the juice is 15 cm deep. When the container is turned upside down, there is a 5 cm gap between the base and the juice level. (a) What is the base area of the container? (b) How much more juice is needed to fill the container completely? (c) After the container is filled completely, all the juice is poured into cups. Each cup holds 225 cm³ and is filled to the brim. How many cups are completely filled?

Area & volumeStructured · 4 marks

A closed rectangular container has the same base area from top to bottom. When it stands upright on its base, it holds 1350 cm³ of orange juice and the juice is 15 cm deep. When the container is turned upside down, there is a 5 cm gap between the base and the juice level.

What is the base area of the container?
How much more juice is needed to fill the container completely?
After the container is filled completely, all the juice is poured into cups. Each cup holds 225 cm³ and is filled to the brim. How many cups are completely filled?

Need a hint?

The gap when the container is upside down is the same size as the empty space at the top when it is upright. What is its base area and height?

Worked answer

(a) Volume = base area × height, so base area = 1350 ÷ 15 = 90 cm².
(b) Upside down, the gap is an empty box with the same base. Its height is 5 cm.
(b) Empty space = 90 × 5 = 450 cm³, so 450 cm³ (450 ml) more juice is needed.
(c) Full capacity = 1350 + 450 = 1800 cm³.
(c) Number of cups = 1800 ÷ 225 = 8.
Answer: (a) 90 cm²; (b) 450 cm³; (c) 8 cups.

Answer: 8 cups

The mistake this question tests

Habit

Left out the units

Many pupils add the 5 cm gap to the volume, or divide 1350 by 225 for part (c). That ignores the extra juice added to fill the container, so the juice poured is not the full capacity.

How to fix it at home →

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