9 self-marking GCSE practice questions on Volume of composite solids, written specifically for AQA, Pearson, OCR across Foundation and Higher tier. Instant marking with full worked solutions on every question.
A few of the 9 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 12 marksGrade 3-4
A solid is made from a cylinder of radius 5 cm and height 6 cm, with a solid hemisphere of the same radius fixed on top. Calculate the total volume of the solid. Give your answer correct to 1 decimal place.
What are the common mistakes in Volume of composite solids?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Omits a hemispheres volume when finding the total volume of a composite solid
Calculated only the cone's volume and forgot to add the hemisphere's volume on top.
Forgets to subtract a cut-out volume when finding a composite solids total volume
Calculated only the cylinder's volume and forgot to subtract the hemispherical dent.
Omits a cones volume when finding the total volume of a composite solid
Calculated only the cylinder's volume and forgot to add the cone's volume on top.
Quick answers about Volume of composite solids
How many Volume of composite solids practice questions are there?
There are 9 self-marking GCSE Maths questions on Volume of composite solids, written for AQA, Pearson, OCR across Foundation and Higher tier. Each one is marked instantly and has a full worked solution.
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No. You can start practising Volume of composite solids straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
Show the worked solution
Volume of composite solid =cylinder volume+hemisphere volume
=πr2h+32πr3
=(π×52×6)+(32π×53)
≈471.24+261.80M1
≈733.0 cm³ A1
Question 22 marksGrade 3-4
A solid block is a cuboid measuring 10 cm by 8 cm by 6 cm. A smaller cuboid measuring 4 cm by 3 cm by 4 cm is cut away from one corner, leaving an L-shaped solid. Calculate the volume of the remaining solid.
Show the worked solution
Volume of remaining solid =large cuboid−cut-away cuboid
=(10×8×6)−(4×3×4)
Question 32 marksGrade 3-4
A cylindrical block of radius 6 cm and height 10 cm has a hemispherical dent of the same radius scooped out of its top face. Calculate the volume of the remaining solid. Give your answer correct to 1 decimal place.
Question 42 marksGrade 3-4
A tent-shaped solid is made from a cuboid measuring 8 cm by 5 cm by 4 cm, with a triangular-prism roof on top. The roof's triangular cross-section has base 5 cm and height 3 cm, and the prism has the same length as the cuboid, 8 cm. Calculate the total volume of the solid.
Question 53 marksGrade 6
The diagram shows a solid shape. The shape is a cone on top of a hemisphere.
Volume of a cone = (1/3)πr²h
Volume of a sphere = (4/3)πr³
The height of the cone is 10 cm. The base of the cone has a diameter of 6 cm. The hemisphere has a diameter of 6 cm.
The total volume of the shape is kπ cm³, where k is an integer.
Work out the value of k.
Question 64 marksGrade 8-9
The base of a cone is fixed to the top of a cylinder to make a decoration. The radius of the base of the cone and of the cylinder is r cm. The cone's height is 5r cm. The total height of the decoration is 6r cm.
The total volume of the decoration is 225 cm³.
Calculate the value of r.