[discia] GCSE Maths › Geometry & Measures › Cylinders

Cylinders

discia.org 10 questions · 38 marks
Name Date
  1. Either paper 2 marks

    Here is a solid cylinder.

    6 cm3 cm

    The radius of the cylinder is \(3\) cm and its height is \(6\) cm.

    Work out the volume of the cylinder. Give your answer in terms of \(\pi\).

    Show answer
    \(54\pi\ \text{cm}^3\)
    Another like this
  2. Calculator 5 marks

    A cardboard cylinder is open at both ends. It has radius \(1.9\) cm and height \(7.5\) cm.

    Harry assumes that the net of its curved surface is a rectangle with length \(l\) cm and height \(7.5\) cm.

    (a)

    Work out the area of Harry's rectangle. Use the \(\pi\) key on your calculator and do not round until your final answer. Give your answer correct to 3 significant figures.

    (b)

    In fact, the net is the parallelogram below, not a rectangle. The parallelogram has the same base \(l\) cm as Harry's rectangle and is the net of the same cylinder.

    l cmDiagram NOT accurately drawn

    How does the area of the rectangle compare with the area of the parallelogram?

    Tick one box.

    - It is equal to the area of the parallelogram - It is less than the area of the parallelogram - It is more than the area of the parallelogram

    (c)

    For the parallelogram and Harry's rectangle, how does the length of a sloping side of the parallelogram compare with the height of the rectangle?

    Tick one box.

    - It is equal to the height of the rectangle - It is less than the height of the rectangle - It is more than the height of the rectangle

    Show answer
    (a) \(89.5\ \text{cm²}\)
    (b) It is equal to the area of the parallelogram
    (c) It is more than the height of the rectangle
    Another like this
  3. Calculator 4 marks

    A drum of cooking oil is in the shape of a cylinder.

    12 cm18 cm

    The drum has a diameter of \(18\) cm and a height of \(12\) cm.

    (a)

    Find the volume of the drum. Give your answer to 1 decimal place.

    (b)

    \(1\) litre \(= 1000\) cm³.

    Work out how many litres the drum holds when it is full. Give your answer to 2 decimal places.

    Show answer
    (a) \(3053.6\ \text{cm}^3\)
    (b) \(3.05\ \text{litres}\)
    Another like this
  4. Either paper 5 marks

    The diagram shows a solid cylinder of radius \(2\) cm and height \(8\) cm.

    8 cm2 cm
    (a)

    Work out the curved surface area of the cylinder. Give your answer in terms of \(\pi\).

    (b)

    Work out the total surface area of the cylinder. Give your answer in terms of \(\pi\).

    Show answer
    (a) \(32\pi\ \text{cm}^2\)
    (b) \(40\pi\ \text{cm}^2\)
    Another like this
  5. Either paper 3 marks

    The diagram shows a cylinder with radius \(5\) cm and height \(h\) cm.

    h cm5 cmDiagram NOT accurately drawn

    The volume of the cylinder is \(425\pi\) cm³.

    Find the value of \(h\).

    Show answer
    \(17\ \text{cm}\)
    Another like this
  6. Either paper 3 marks

    Here is a cylinder with radius \(r\) cm and height \(20\) cm.

    20 cmr cmDiagram NOT accurately drawn

    The volume of the cylinder is \(500\pi\) cm³.

    Find the value of \(r\).

    Show answer
    \(5\ \text{cm}\)
    Another like this
  7. Calculator 4 marks

    Ben has 5 identical cylindrical tanks on his farm. Each tank has a diameter of \(80\) cm and a height of \(140\) cm.

    140 cm80 cm

    The 5 tanks are to be filled completely with a mixture of fertiliser and water. The fertiliser has to be mixed with water in the ratio \(1 : 100\) by volume. Ben has \(35.1\) litres of fertiliser.

    \(1\) litre \(= 1000\ \text{cm}^3\).

    Does Ben have enough fertiliser for the 5 tanks? Give a reason for your answer.

    Show answer
    Yes — the tanks need \(34.8\) litres of fertiliser and Ben has \(35.1\) litres.
    Another like this
  8. Calculator 5 marks

    Amara has to cover 4 identical tanks completely with paint. Each tank is in the shape of a cylinder with a top and a bottom, with a diameter of \(3\) m and a height of \(4\) m.

    4 m3 m

    One tin of paint covers \(3\ \text{m}^2\). She has 60 tins of paint.

    Does Amara have enough paint to cover 4 tanks completely? You must show how you get your answer.

    Show answer
    No — the tanks need \(207.35\ \text{m}^2\) of paint and she only has \(180\ \text{m}^2\) available.
    Another like this
  9. Either paper 2 marks

    Here is a solid cylinder.

    9 cm8 cm

    The radius of the cylinder is \(8\) cm and its height is \(9\) cm.

    Find the volume of the cylinder. Give your answer in terms of \(\pi\).

    Show answer
    \(576\pi\ \text{cm}^3\)
    Another like this
  10. Calculator 5 marks

    A cardboard cylinder is open at both ends. It has radius \(1.1\) cm and height \(12.4\) cm.

    Harry assumes that the net of its curved surface is a rectangle with length \(l\) cm and height \(12.4\) cm.

    (a)

    Find the area of Harry's rectangle. Use the \(\pi\) key on your calculator and do not round until your final answer. Give your answer correct to 3 significant figures.

    (b)

    In fact, the net is the parallelogram below, not a rectangle. The parallelogram has the same base \(l\) cm as Harry's rectangle and is the net of the same cylinder.

    l cmDiagram NOT accurately drawn

    How does the length of a sloping side of the parallelogram compare with the height of the rectangle?

    Tick one box.

    - It is less than the height of the rectangle - It is equal to the height of the rectangle - It is more than the height of the rectangle

    (c)

    For the parallelogram and Harry's rectangle, how does the perpendicular height of the parallelogram compare with the height of the rectangle?

    Tick one box.

    - It is equal to the height of the rectangle - It is more than the height of the rectangle - It is less than the height of the rectangle

    Show answer
    (a) \(85.7\ \text{cm²}\)
    (b) It is more than the height of the rectangle
    (c) It is equal to the height of the rectangle
    Another like this
discia.org Cylinders · sheet 1
Answers Cylinders · sheet 1
  1. \(54\pi\ \text{cm}^3\)
  2. (a) \(89.5\ \text{cm²}\)
    (b) It is equal to the area of the parallelogram
    (c) It is more than the height of the rectangle
  3. (a) \(3053.6\ \text{cm}^3\)
    (b) \(3.05\ \text{litres}\)
  4. (a) \(32\pi\ \text{cm}^2\)
    (b) \(40\pi\ \text{cm}^2\)
  5. \(17\ \text{cm}\)
  6. \(5\ \text{cm}\)
  7. Yes — the tanks need \(34.8\) litres of fertiliser and Ben has \(35.1\) litres.
  8. No — the tanks need \(207.35\ \text{m}^2\) of paint and she only has \(180\ \text{m}^2\) available.
  9. \(576\pi\ \text{cm}^3\)
  10. (a) \(85.7\ \text{cm²}\)
    (b) It is more than the height of the rectangle
    (c) It is equal to the height of the rectangle
discia.org Cylinders · sheet 1