Area & Volume

16 Grade 9 Mathematics questions on Area & Volume, with worked marking schemes. 16 questions are available on this topic in full.

1. Question 1

   1 mark

   The volume of a cuboid 5 cm × 4 cm × 3 cm is ___

   A. 12 cm³

   B. 94 cm³

   C. 47 cm³

   D. 60 cm³

   (1 mark)

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2. Question 2

   4 marks

   Find the shaded area between two concentric circles with outer radius 10 cm and inner radius 6 cm. (π ≈ 3.14)

   (4 marks)

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3. Question 3

   1 mark

   The circumference of a circle with diameter 14 cm is ___ (use π ≈ 22/7)

   A. 44 cm

   B. 22 cm

   C. 154 cm

   D. 88 cm

   (1 mark)

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4. Question 4

   1 mark

   The density of an object with mass 120 g and volume 40 cm³ is ___

   A. 0.33 g/cm³

   B. 80 g/cm³

   C. 3 g/cm³

   D. 4,800 g/cm³

   (1 mark)

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5. Question 5

   1 mark

   A cone has base radius 3 cm and height 4 cm. Its volume is ___ (use π ≈ 3.14)

   A. 12.56 cm³

   B. 75.36 cm³

   C. 113.04 cm³

   D. 37.68 cm³

   (1 mark)

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6. Question 6

   1 mark

   Area of a trapezium with parallel sides 8 cm and 12 cm, height 5 cm is ___

   A. 40 cm²

   B. 100 cm²

   C. 60 cm²

   D. 50 cm²

   (1 mark)

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7. Question 7

   1 mark

   A rectangular prism has length 8 m, width 5 m, and height 3 m. Its volume is ___

   A. 40 m³

   B. 136 m³

   C. 79 m³

   D. 120 m³

   (1 mark)

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8. Question 8

   1 mark

   The volume of a cylinder with radius 7 cm and height 10 cm is ___ (π ≈ 22/7)

   A. 440 cm³

   B. 1,540 cm³

   C. 154 cm³

   D. 770 cm³

   (1 mark)

   Marking scheme

   B. $1,540$ cm${}^3$ — a cylinder's volume is the circular cross-section times the height: $\pi r^{2}h=\frac{22}{7}\times 49\times 10$. C stops at the area of the circle and never multiplies by the height.

9. Question 9

   1 mark

   The area of a triangle with base 10 cm and height 6 cm is ___

   A. 60 cm²

   B. 120 cm²

   C. 30 cm²

   D. 15 cm²

   (1 mark)

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10. Question 10

    1 mark

    The area of a circle with radius 7 cm is ___ (use π ≈ 22/7)

    A. 44 cm²

    B. 49 cm²

    C. 22 cm²

    D. 154 cm²

    (1 mark)

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11. Question 11

    3 marks

    An object has mass 500 g and volume 250 cm³. Find its density and state whether it will float in water (density of water = 1 g/cm³).

    (3 marks)

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12. Question 12

    4 marks

    A metallic sphere has volume 288π cm³. Find its radius.

    (4 marks)

    Marking scheme

    The volume of a sphere is $V=\frac{4}{3}\pi r^3$, and here $V=288\pi$. (1)

    So $\frac{4}{3}\pi r^3=288\pi$. Divide both sides by $\pi$: $\frac{4}{3}{r}^3=288$. (1)

    Multiply both sides by $\frac{3}{4}$: $r^3=288\times \frac{3}{4}=216$. (1)

    Take the cube root: $r=\sqrt[3]{216}=6$, since $6\times 6\times 6=216$. (1)

    Final answer: $6$ cm.

13. Question 13

    3 marks

    A cylindrical water tank at a school has a radius of $1.4$ m and a height of $2$ m. Taking $\pi =\frac{22}{7}$, calculate the volume of water it can hold when full, in cubic metres.

    (3 marks)

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14. Question 14

    1 mark

    The total surface area of a cube with side 4 cm is ___

    A. 48 cm²

    B. 64 cm²

    C. 16 cm²

    D. 96 cm²

    (1 mark)

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15. Question 15

    3 marks

    A garden is shaped like a trapezium with parallel sides of 15 m and 9 m, and a perpendicular height of 8 m. Find the area of the garden.

    (3 marks)

    Marking scheme

    The area of a trapezium is $\frac{1}{2}(a+b)h$, where $a$ and $b$ are the parallel sides and $h$ is the perpendicular height. (1)

    Add the parallel sides: $15+9=24$ m. (1)

    Substitute: $\frac{1}{2}\times 24\times 8=12\times 8=96$. (1)

    Final answer: $96$ m${}^2$.

16. Question 16

    5 marks

    A cylindrical water tank has radius 3.5 m and height 4 m. Find its volume and the mass of water it holds. (1 m³ = 1,000 litres; density of water = 1 kg/L; π ≈ 22/7)

    (5 marks)

    Marking scheme

    The volume of a cylinder is $V=\pi r^{2}h$. (1)

    With $r=3.5$ m, $r^2=12.25$ m${}^2$. (1)

    Substitute: $V=\frac{22}{7}\times 12.25\times 4=38.5\times 4=154$ m${}^3$. (1)

    Convert to litres, using $1$ m${}^3=1,000$ litres: $154\times 1,000=154,000$ litres. (1)

    Water has a mass of $1$ kg per litre, so the mass is $154,000\times 1=154,000$ kg. (1)

    Final answer: the volume is $154$ m${}^3$ ($154,000$ litres) and the mass is $154,000$ kg.

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