Volume and Capacity

14 Grade 10 Essential Mathematics questions on Volume and Capacity, with worked marking schemes. 14 questions are available on this topic in full.

1. Question 1

   1 mark

   A conical funnel used for filling bottles has a base radius of 7 cm and a vertical height of 12 cm. Taking $\pi =\frac{22}{7}$, what volume of liquid does it hold when full?

   A. 616 cm³

   B. 1 848 cm³

   C. 88 cm³

   D. 205.3 cm³

   (1 mark)

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2. Question 2

   4 marks

   A cylindrical storage tank has a radius of 0.7 m and a height of 2 m. Taking $\pi =\frac{22}{7}$, determine its capacity in litres and the time taken to fill it from empty by a pipe delivering 22 litres per minute.

   (4 marks)

   Marking scheme

   1. Volume = $\pi r^{2}h=\frac{22}{7}\times 0.7\times 0.7\times 2=3.08m^3$ (1 mark). 2. Capacity = $3.08\times 1000=3080$ litres (1 mark). 3. Time = $3080÷22=140$ minutes (1 mark). 4. = 2 hours 20 minutes (1 mark).

3. Question 3

   1 mark

   A rectangular water container in a school laboratory measures 80 cm by 50 cm by 40 cm. What is its capacity in litres?

   A. 160 litres

   B. 16 litres

   C. 1 600 litres

   D. 160 000 litres

   (1 mark)

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4. Question 4

   1 mark

   A cattle water trough has a uniform triangular cross-section of base 1.2 m and vertical depth 0.5 m, and is 4 m long. What is its capacity in litres when filled to the brim?

   A. 1 200 litres

   B. 120 litres

   C. 600 litres

   D. 2 400 litres

   (1 mark)

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5. Question 5

   1 mark

   A spherical float in a water tank has a radius of 21 cm. Taking $\pi =\frac{22}{7}$, what is its volume?

   A. 5 544 cm³

   B. 38 808 cm³

   C. 9 702 cm³

   D. 29 106 cm³

   (1 mark)

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6. Question 6

   4 marks

   A school has 450 learners, each using an average of 8 litres of water per day. The school stores water in a tank of capacity 18 m³. Calculate how many full days the tank will serve the learners when it is full.

   (4 marks)

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7. Question 7

   1 mark

   A tap delivers water at a steady rate of 15 litres per minute into an empty tank of capacity 1 800 litres. How long does the tank take to fill?

   A. 1 hour 20 minutes

   B. 12 minutes

   C. 2 hours

   D. 3 hours

   (1 mark)

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8. Question 8

   3 marks

   State the relationship between the volume of a cone and the volume of a cylinder having the same base radius and the same height, and describe a simple activity a learner can carry out to verify it.

   (3 marks)

   Marking scheme

   1. The volume of the cone is one third the volume of the cylinder, that is V(cone) = $\frac{1}{3}\pi r^{2}h$ (1 mark). 2. Activity: fill the open cone to the brim with dry sand or water and empty it into the cylinder of the same base radius and height, repeating until the cylinder is full (1 mark). 3. The cylinder is filled after exactly three coneloads, confirming the one-third relationship (1 mark).

9. Question 9

   2 marks

   Distinguish between the volume and the capacity of a container.

   (2 marks)

   Marking scheme

   1. Volume is the amount of space the container occupies or encloses, measured in cubic units such as cm³ or m³ (1 mark). 2. Capacity is the amount of liquid the container can hold, measured in units such as millilitres or litres (1 mark). Accept a correct statement of the link, e.g. 1 000 cm³ holds 1 litre, as part of either point.

10. Question 10

    5 marks

    A cylindrical drum of radius 0.35 m is filled with water to a height of 1 m. All the water is poured into an empty rectangular tank whose base measures 1.5 m by 0.8 m. Taking $\pi =\frac{22}{7}$, calculate the depth of water in the tank.

    (5 marks)

    Marking scheme

    1. Volume of water = $\pi r^{2}h=\frac{22}{7}\times 0.35\times 0.35\times 1$ (1 mark for correct substitution). 2. Volume = 0.385 m³ (1 mark). 3. Base area of the tank = $1.5\times 0.8=1.2m^2$ (1 mark). 4. Since the volume of water is unchanged on pouring, $1.2\times d=0.385$ (1 mark). 5. Depth $d=0.385÷1.2=0.321m$ (32.1 cm) (1 mark).

11. Question 11

    1 mark

    A cylindrical tank on a poultry farm has a radius of 1.4 m and a height of 2 m. Taking $\pi =\frac{22}{7}$, what is its capacity in litres?

    A. 12.32 litres

    B. 12 320 litres

    C. 12 320 000 litres

    D. 1 232 litres

    (1 mark)

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12. Question 12

    1 mark

    A cooling tank at a milk collection centre has a volume of 4.5 m³. What is its capacity in litres?

    A. 450 litres

    B. 4 500 litres

    C. 4 500 000 litres

    D. 45 000 litres

    (1 mark)

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13. Question 13

    3 marks

    Harvested maize is heaped on a drying yard in the shape of a cone of base diameter 4.2 m and vertical height 1.5 m. Taking $\pi =\frac{22}{7}$, calculate the volume of the heap.

    (3 marks)

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14. Question 14

    3 marks

    A rectangular fish pond measures 6 m long and 4 m wide and is 1.5 m deep. Water in it stands at a depth of 1.2 m. Calculate the volume of water in the pond in cubic metres and state its capacity in litres.

    (3 marks)

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