[discia] GCSE Maths › Geometry & Measures › Surface Area

Surface Area

discia.org 10 questions · 31 marks
Name Date
  1. Either paper 2 marks

    The diagram shows a cube. The dashed lines are the edges you cannot see from this side.

    2 cm

    Each edge of the cube is \(2\) cm long.

    Find the total surface area of the cube.

    Show answer
    \(24\ \text{cm²}\)
    Another like this
  2. Either paper 2 marks

    Here is a cuboid.

    5 cm4 cm2 cm

    Part of the net of the cuboid has been drawn for you on the centimetre grid. The rectangle with its bottom left corner at \((4, 3)\) is the base of the cuboid.

    Two faces are missing. One is joined to the left edge of the base. The other is joined to the top edge of the rectangle above the base.

    Complete the net: plot the four corners of each missing face on the grid, including any corner that is already a corner of the net.

    123456789101112131415161712345678910111213141516170xy
    Show answer
    Face 1: a rectangle 2 cm wide and 4 cm high to the left of the base, with opposite corners at (2, 3) and (4, 7). Face 2: a rectangle 5 cm wide and 4 cm high above the rectangle that is above the base, with opposite corners at (4, 9) and (9, 13).
    123456789101112131415161712345678910111213141516170xy
    Another like this
  3. Either paper 3 marks

    Here is a cuboid.

    8 cm5 cm9 cm

    Calculate the total surface area of the cuboid.

    Show answer
    \(314\ \text{cm²}\)
    Another like this
  4. Either paper 2 marks

    Here is cuboid \(A\).

    8 cm6 cm7 cmA

    Cuboid \(B\) is made by joining two cuboids like \(A\), so that the faces measuring \(6\) cm by \(7\) cm are touching.

    B

    Not drawn accurately.

    Volume of \(A\) : volume of \(B\) = \(1 : 2\)

    Callum says, "The surface area of B is more than 1.8 times the surface area of A."

    Is Callum correct?

    Tick one box.

    Yes / No / Cannot tell

    Give a reason for your answer.

    Show answer
    No. The two faces that are joined are hidden, so \(SA(B) = 2 \times 292 - 2 \times 42 = 500\) cm². This is less than \(1.8 \times 292 = 525.6\) cm², which is \(1.8\) times \(SA(A)\).
    Another like this
  5. Either paper 3 marks

    Here is a cuboid.

    54 cm1.37 m1.1 m

    Work out the total surface area of the cuboid.

    Give your answer in square metres.

    Show answer
    \(5.6816\ \text{m²}\)
    Another like this
  6. Either paper 4 marks

    Here is a solid prism that is \(14\) cm long.

    14 cm

    The cross-section of the prism is a right-angled triangle with sides \(3\) cm, \(4\) cm and \(5\) cm. The right angle is between the \(3\) cm side and the \(4\) cm side.

    Find the total surface area of the prism.

    Show answer
    \(180\ \text{cm²}\)
    Another like this
  7. Either paper 3 marks

    The diagram shows a solid cube placed on a horizontal table.

    The force exerted by the cube on the table is \(196\) newtons. The pressure on the table due to the cube is \(4\) newtons/cm².

    \(\text{pressure} = \text{force} \div \text{area}\)

    Show that the total surface area of the cube is less than \(310\) cm².

    Show answer
    \(\text{base area} = 196 \div 4 = 49\) cm², so \(\text{total surface area} = 6 \times 49 = 294\) cm², and \(294 < 310\).
    Another like this
  8. Either paper 4 marks

    A solid cube has a total surface area of \(486\) cm².

    Find the volume of the solid.

    Show answer
    \(729\ \text{cm³}\)
    Another like this
  9. Either paper 5 marks

    The diagram shows a cuboid. The height of the cuboid is \(h\) cm.

    6 cm4 cmh cmDiagram NOT accurately drawn
    (a)

    Assume that the total surface area of the cuboid is \(108\) cm².

    Work out the volume of the cuboid.

    (b)

    In fact, the total surface area of the cuboid is larger than \(108\) cm².

    What does this mean about the volume of the cuboid?

    Tick one box and give a reason for your answer.

    - It is bigger than the answer to part (a) - It is smaller than the answer to part (a) - It is the same as the answer to part (a) - It could be any of the above

    Show answer
    (a) \(72\ \text{cm³}\)
    (b) It is bigger than the answer to part (a), because 6 cm and 4 cm stay the same, so the volume changes only with h, which is larger
    Another like this
  10. Either paper 3 marks

    The diagram shows a cube and a cuboid.

    3 cm 5 cm4 cm7 cm

    The cube is placed on the top face of the cuboid to make a solid. The whole of the base of the cube is on the top face of the cuboid.

    The diagrams are not drawn to scale.

    Calculate the total surface area of the solid.

    Show answer
    \(202\ \text{cm²}\)
    Another like this
discia.org Surface Area · sheet 1
Answers Surface Area · sheet 1
  1. \(24\ \text{cm²}\)
  2. Face 1: a rectangle 2 cm wide and 4 cm high to the left of the base, with opposite corners at (2, 3) and (4, 7). Face 2: a rectangle 5 cm wide and 4 cm high above the rectangle that is above the base, with opposite corners at (4, 9) and (9, 13).
    123456789101112131415161712345678910111213141516170xy
  3. \(314\ \text{cm²}\)
  4. No. The two faces that are joined are hidden, so \(SA(B) = 2 \times 292 - 2 \times 42 = 500\) cm². This is less than \(1.8 \times 292 = 525.6\) cm², which is \(1.8\) times \(SA(A)\).
  5. \(5.6816\ \text{m²}\)
  6. \(180\ \text{cm²}\)
  7. \(\text{base area} = 196 \div 4 = 49\) cm², so \(\text{total surface area} = 6 \times 49 = 294\) cm², and \(294 < 310\).
  8. \(729\ \text{cm³}\)
  9. (a) \(72\ \text{cm³}\)
    (b) It is bigger than the answer to part (a), because 6 cm and 4 cm stay the same, so the volume changes only with h, which is larger
  10. \(202\ \text{cm²}\)
discia.org Surface Area · sheet 1