Surface Area of Solids

14 Grade 10 Essential Mathematics questions on Surface Area of Solids, with worked marking schemes. 14 questions are available on this topic in full.

1. Question 1

   2 marks

   Explain why a company that packs milk in cylindrical tins is interested in the total surface area of each tin.

   (2 marks)

   Marking scheme

   1. The total surface area gives the amount of metal sheet needed per tin, which determines the cost of materials and helps the company use the least metal for a given capacity (1 mark). 2. It also determines the size of the label or printed wrapper that must cover the tin (1 mark). Accept any other valid reason tied to area, e.g. the amount of coating or lacquer applied to the surface.

2. Question 2

   1 mark

   A spherical plastic ball used in a school games lesson has a radius of 10.5 cm. Taking $\pi =\frac{22}{7}$, what is its surface area?

   A. 346.5 cm²

   B. 1 386 cm²

   C. 4 851 cm²

   D. 693 cm²

   (1 mark)

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3. Question 3

   1 mark

   A closed rectangular metal box used for packing biscuits measures 40 cm by 30 cm by 20 cm. What is its total surface area?

   A. 2 600 cm²

   B. 10 400 cm²

   C. 5 200 cm²

   D. 4 800 cm²

   (1 mark)

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4. Question 4

   1 mark

   A rectangular farm store measures 5 m long, 4 m wide and 3 m high. Only the four walls are to be plastered. What is the area to be plastered?

   A. 54 m²

   B. 94 m²

   C. 27 m²

   D. 74 m²

   (1 mark)

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5. Question 5

   3 marks

   A water tank for a school kitchen garden is a cylinder open at the top, of radius 1.4 m and height 2.5 m. Taking $\pi =\frac{22}{7}$, calculate the area of metal sheet used to make it.

   (3 marks)

   Marking scheme

   1. Curved surface area = $2\pi rh=2\times \frac{22}{7}\times 1.4\times 2.5=22m^2$ (1 mark). 2. Area of the base = $\pi r^2=\frac{22}{7}\times 1.4\times 1.4=6.16m^2$ (1 mark). 3. Area of metal sheet = $22+6.16=28.16m^2$ (1 mark). The tank is open at the top, so no top circle is included.

6. Question 6

   1 mark

   A wooden cube used as a display block has a total surface area of 150 cm². What is the length of one edge of the cube?

   A. 5 cm

   B. 12.5 cm

   C. 6.25 cm

   D. 25 cm

   (1 mark)

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7. Question 7

   1 mark

   A closed cylindrical water tank at a home in Machakos has a radius of 0.7 m and a height of 2 m. Taking $\pi =\frac{22}{7}$, what is the total surface area of the tank?

   A. 11.88 m²

   B. 8.80 m²

   C. 5.94 m²

   D. 10.34 m²

   (1 mark)

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8. Question 8

   2 marks

   Distinguish between the curved surface area and the total surface area of a closed cylinder.

   (2 marks)

   Marking scheme

   1. Curved surface area is the area of the rectangular sheet that wraps round the cylinder only, given by 2πrh (1 mark). 2. Total surface area is the curved surface area together with the areas of the two circular ends, given by $2\pi rh+2\pi r^2$ (1 mark).

9. Question 9

   1 mark

   A decorated conical hat made for a cultural day has a base radius of 7 cm and a slant height of 25 cm. Taking $\pi =\frac{22}{7}$, what is the area of the material forming the curved surface only?

   A. 154 cm²

   B. 550 cm²

   C. 704 cm²

   D. 1 100 cm²

   (1 mark)

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10. Question 10

    3 marks

    The roof of a circular granary is a cone of base radius 2 m and slant height 3.5 m. Taking $\pi =\frac{22}{7}$, calculate the area of iron sheet needed for the roof and the number of sheets required if each sheet covers 2 m².

    (3 marks)

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11. Question 11

    1 mark

    A carpenter makes two cubes. The edge of the second cube is twice the edge of the first cube. The total surface area of the second cube is the total surface area of the first cube multiplied by:

    A. 8

    B. 2

    C. 4

    D. 6

    (1 mark)

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12. Question 12

    4 marks

    A classroom measures 8 m by 6 m and is 3 m high. The four walls and the ceiling are to be painted. One litre of paint covers 11 m² and costs KSh 450. Calculate the cost of the paint required.

    (4 marks)

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13. Question 13

    4 marks

    A gift box is a cube of edge 25 cm. Wrapping paper is to cover the whole box, with an extra 10% of the surface area allowed for overlaps. Calculate the area of wrapping paper required.

    (4 marks)

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14. Question 14

    4 marks

    A grain silo standing on the ground consists of a cylinder of radius 1.4 m and height 4 m, with a conical top of slant height 2 m. Taking $\pi =\frac{22}{7}$, calculate the outer surface area to be painted, excluding the base which rests on the ground.

    (4 marks)

    Marking scheme

    1. Curved surface area of cylinder = $2\pi rh=2\times \frac{22}{7}\times 1.4\times 4$ (1 mark for correct substitution). 2. = 35.2 m² (1 mark). 3. Curved surface area of cone = $\pi rl=\frac{22}{7}\times 1.4\times 2=8.8m^2$ (1 mark). 4. Total area painted = $35.2+8.8=44m^2$ (1 mark).

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