Volume & Capacity

7 Grade 7 Mathematics questions on Volume & Capacity, with worked marking schemes. 7 questions are available on this topic in full.

1. Question 1

   4 marks

   A cylindrical tank has diameter 1.4 m and height 2 m. Find its capacity in litres. (Use $\pi =\frac{22}{7}$, 1 m³ = 1,000 L)

   (4 marks)

   Marking scheme

   The radius is half the diameter: $r=\frac{1.4}{2}=0.7$ m. (1)

   The volume of a cylinder is $\pi r^{2}h$, so $V=\frac{22}{7}\times 0.7^2\times 2$. (1)

   $0.7^2=0.49$, and $\frac{22}{7}\times 0.49=1.54$, so $V=1.54\times 2=3.08$ m${}^3$. (1)

   Capacity in litres: $3.08\times 1,000=3,080$. (1)

   Final answer: $3,080$ litres.

2. Question 2

   3 marks

   The cross-section of a prism is a triangle with base 6 cm and height 4 cm. The prism is 15 cm long. Find the volume.

   (3 marks)

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3. Question 3

   1 mark

   How many litres does a 30 cm × 20 cm × 15 cm box hold? (1L = 1000 cm³)

   A. 9 litres

   B. 0.9 litres

   C. 900 litres

   D. 90 litres

   (1 mark)

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4. Question 4

   3 marks

   A rectangular tank 2 m × 1.5 m × 1 m is full. Water is poured into bottles of 500 ml each. How many bottles?

   (3 marks)

   Marking scheme

   The volume of a cuboid is length $\times$ width $\times$ height: $2\times 1.5\times 1=3$ m${}^3$. (1)

   Change to millilitres, since the bottles are in ml. $1$ m${}^3=1,000$ litres and $1$ litre $=1,000$ ml, so $3$ m${}^3=3,000,000$ ml. (1)

   Divide by the size of one bottle: $3,000,000÷500=6,000$. (1)

   Final answer: $6,000$ bottles.

5. Question 5

   1 mark

   A cuboid is 12 cm × 8 cm × 5 cm. Volume = ?

   A. 960 cm³

   B. 480 cm³

   C. 400 cm³

   D. 120 cm³

   (1 mark)

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6. Question 6

   1 mark

   A cylinder has radius 7 cm and height 10 cm. Find the volume. ($\pi =\frac{22}{7}$)

   A. 440 cm³

   B. 770 cm³

   C. 3,080 cm³

   D. 1,540 cm³

   (1 mark)

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7. Question 7

   1 mark

   The volume of a cube is 343 cm³. What is the side?

   A. 7 cm

   B. 12 cm

   C. 49 cm

   D. 14 cm

   (1 mark)

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