Volume units and capacity questions with answers

Questions

1. Question 1m³ and cm³

   A container holds $3.75$ m³. Express this volume in cm³.

   Show the worked solution

   1. Step 1: 1 m = 100 cm, so cube it for volume$1 \text{ m}^3 = 100 \times 100 \times 100 \text{ cm}^3$$= 1\,000\,000 \text{ cm}^3$
   2. Step 2: Change to cm³: multiply or divide?$3.75 \text{ m}^3 = 3.75 \times 1\,000\,000 \text{ cm}^3$$= 3\,750\,000$ cm³
2. Question 2cm³ and litres

   A container holds $300$ cm³ of water. Express this in litres.

   Show the worked solution

   1. Step 1: 1 litre = 1000 cm³ (and 1 ml = 1 cm³)$1 \text{ litre} = 1000 \text{ cm}^3$
   2. Step 2: Change cm³ to litres: multiply or divide?$300 \text{ cm}^3 = \dfrac{300}{1000} \text{ litres}$$= 0.3$ litres
3. Question 3Capacity of a tank

   A rectangular aquarium measures $40$ cm by $25$ cm by $30$ cm. Find its capacity, in litres.

   Show the worked solution

   1. Step 1: Volume of the tank in cm³$V = 40 \times 25 \times 30$$= 30\,000$ cm³
   2. Step 2: Change cm³ to litres$\text{Capacity} = \dfrac{30000}{1000}$$= 30$ litres
4. Question 4Time to fill a tank

   A cuboid container measures $120$ cm by $50$ cm by $40$ cm. It is empty, and water flows in from a tap at $8$ litres per minute. Find the time, in minutes, taken to fill it completely.

   Show the worked solution

   1. Step 1: Volume of the tank in cm³$V = 120 \times 50 \times 40$$= 240\,000$ cm³
   2. Step 2: Change cm³ to litres$\text{Capacity} = \dfrac{240000}{1000}$$= 240$ litres
   3. Step 3: Time = capacity ÷ rate$\text{Time} = \dfrac{240}{8}$$= 30$ minutes
5. Question 5Depth of water in a tank

   A cuboid container has a rectangular base measuring $80$ cm by $50$ cm. $60$ litres of water are poured into it when it is empty. Find the depth of the water, $d$ cm.

   Show the worked solution

   1. Step 1: Change the water's volume to cm³$60 \text{ litres} = 60 \times 1000 \text{ cm}^3$$= 60000 \text{ cm}^3$
   2. Step 2: Volume of water = base area × depth$80 \times 50 \times d = 60000$$d = \dfrac{60000}{4000}$$d = 15$
6. Question 6A cross-section from a filling rate

   The diagram shows a water trough in the shape of a prism of length $80$ cm. It is empty, and water flows in at a constant rate of $4$ litres per minute. It is full after $6$ minutes. Find the area of its cross-section, in cm².

   Show the worked solution

   1. Step 1: Volume of water = rate × time$\text{Volume} = 4 \times 6$$\phantom{\text{Volume}} = 24$ litres
   2. Step 2: 1 litre = 1000 cm³$24 \text{ litres} = 24 \times 1000$$\phantom{24 \text{ litres}} = 24000$ cm³
   3. Step 3: Volume of a prism = area of cross-section × length: divide by the length$A = \dfrac{24000}{80}$$\phantom{A} = 300$ cm²