Common Solids

13 Grade 8 Mathematics questions on Common Solids, with worked marking schemes. 13 questions are available on this topic in full.

1. Question 1

   3 marks

   A cylinder has radius 3.5 cm and height 10 cm. Taking pi = 22/7, find its volume.

   (3 marks)

   Marking scheme

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

   With $r=3.5$ cm: $r^2=12.25$, and $\frac{22}{7}\times 12.25=38.5$ cm${}^2$ for the base area. (1)

   Multiply by the height: $38.5\times 10=385$. (1)

   Final answer: $385$ cm${}^3$.

2. Question 2

   1 mark

   Find the volume of a cuboid measuring 5 cm by 4 cm by 3 cm.

   A. 12 cm³

   B. 27 cm³

   C. 60 cm³

   D. 120 cm³

   (1 mark)

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3. Question 3

   1 mark

   How many edges does a cuboid have?

   A. 12

   B. 6

   C. 8

   D. 4

   (1 mark)

   Marking scheme

   A. $12$ — four edges round the top, four round the bottom and four uprights. C is its number of vertices and B its number of faces. Faces, edges and vertices are the three counts most easily swapped for one another.

4. Question 4

   3 marks

   A cuboid measures 8 cm by 5 cm by 4 cm.

   (a) Find its volume. (1 mark)

   (b) Find its total surface area. (2 marks)

   Marking scheme

   (a) The volume of a cuboid is length $\times$ width $\times$ height: $8\times 5\times 4=160$ cm${}^3$. (1)

   (b) A cuboid has three pairs of identical faces, so the surface area is $2(lw+lh+wh)$. (1)

   Substitute: $lw=40$, $lh=32$, $wh=20$, so $2(40+32+20)=2\times 92=184$. (1)

   Final answer: the volume is $160$ cm${}^3$ and the surface area is $184$ cm${}^2$.

5. Question 5

   1 mark

   A cuboid has a volume of 120 cm³ and a base area of 24 cm². Find its height.

   A. 5 cm

   B. 96 cm

   C. 2880 cm

   D. 4 cm

   (1 mark)

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6. Question 6

   1 mark

   Find the volume of a cube of side 4 cm.

   A. 16 cm³

   B. 64 cm³

   C. 12 cm³

   D. 48 cm³

   (1 mark)

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7. Question 7

   1 mark

   Find the volume of a cube of side 6 cm.

   A. 36 cm³

   B. 216 cm³

   C. 18 cm³

   D. 72 cm³

   (1 mark)

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8. Question 8

   1 mark

   How many vertices does a triangular prism have?

   A. 5

   B. 9

   C. 8

   D. 6

   (1 mark)

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9. Question 9

   1 mark

   The net of a cube is made up of how many squares?

   A. 4

   B. 8

   C. 12

   D. 6

   (1 mark)

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10. Question 10

    3 marks

    A cylindrical tank has radius 7 m and height 4 m. Taking pi = 22/7, find its volume in cubic metres.

    (3 marks)

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11. Question 11

    1 mark

    How many faces does a triangular prism have?

    A. 4

    B. 6

    C. 5

    D. 9

    (1 mark)

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12. Question 12

    1 mark

    How many faces does a cube have?

    A. 4

    B. 8

    C. 6

    D. 12

    (1 mark)

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13. Question 13

    1 mark

    Find the volume of a cylinder of radius 7 cm and height 10 cm. (Take pi = 22/7)

    A. 1540 cm³

    B. 154 cm³

    C. 220 cm³

    D. 3080 cm³

    (1 mark)

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