GCSE Revision - Volume and Surface Area
[Nov 2013 Calc] 24.The diagram shows a large tin of pet food in the shape of a cylinder.
The large tin has a radius of 6.5 cm and a height of 11.5 cm.A pet food company wants to make a new size of tin.The new tin will have a radius of 5.8 cm.It will have the same volume as the large tin.
Calculate the height of the new tin.Give your answer correct to one decimal place.
...... cm
(Total for Question 24 is 3 marks)
[Nov 2013 NonCalc] 3. Here is a triangular prism.
Work out the volume of this triangular prism.
......
(Total for Question 3 is 4 marks)
[March 2013 Calc] 22.
A frustum is made by removing a small cone from a similar large cone.
The height of the small cone is 20 cm.The height of the large cone is 40 cm.
The diameter of the base of the large cone is 30 cm.
Work out the volume of the frustum.Give your answer correct to 3 significant figures.
...... cm3
(Total for Question 22 is 4 marks)
[March 2013 Calc] 9.Here is a solid prism.
Work out the volume of the prism.
...... cm3
(Total for Question 9 is 3 marks)
[March 2013 NonCalc] 23. The diagram shows a solid hemisphere of radius 5 cm.
Find the total surface area of the solid hemisphere.
Give your answer in terms of .
...... cm2
(Total for Question 23 is 3 marks)
[June 2013 NonCalc] 17. Sumeet has a pond in the shape of a prism.
The pond is completely full of water.Sumeet wants to empty the pond so he can clean it.
Sumeet uses a pump to empty the pond.
The volume of water in the pond decreases at a constant rate.
The level of the water in the pond goes down by 20 cm in the first 30 minutes.
Work out how much more time Sumeet has to wait for the pump to empty the pond completely.
......
(Total for Question 17 is 6 marks)
[Nov 2012 Calc] 23. The diagram shows a pyramid.
BCDE is a square with sides of length 10 cm.
The other faces of the pyramid are equilateral triangles with sides of length 10 cm.
(a) Calculate the volume of the pyramid.
Give your answer correct to 3 significant figures.
...... cm3
(4)
(b) Find the size of angle DAB.
...... °
(2)
[Nov 2012 Calc] 13. The diagram shows a solid triangular prism.
The prism is made from metal.The density of the metal is 6.6 grams per cm3.
Calculate the mass of the prism.
...... grams
(Total for Question 13 is 3 marks)
[Nov 2012 Calc] 11. The diagram shows a cube and a cuboid.
All the measurements are in cm.
The volume of the cube is 100 cm3 more than the volume of the cuboid.
(a)Show that x3 – 10x = 100
(2)
(b) Use a trial and improvement method to find the value of x.
Give your answer correct to 1 decimal place.
You must show all your working.
x = ......
(4)
[June 2012 NonCalc] 25. The diagram shows a solid metal cylinder.
The cylinder has base radius 2x and height 9x.The cylinder is melted down and made into a sphere of radius r.Find an expression for r in terms of x.
......
(Total for Question 25 is 3 marks)
[June 2012 NonCalc] 12. Jane has a carton of orange juice.
The carton is in the shape of a cuboid.
The depth of the orange juice in the carton is 8 cm.
Jane closes the carton.
Then she turns the carton over so that it stands on the shaded face.
Work out the depth, in cm, of the orange juice now.
...... cm
(Total for Question 12 is 3 marks)
[Nov 2011 Calc] 24. The diagram shows a solid hemisphere of radius 8 cm.
Work out the total surface area of the hemisphere.
Give your answer correct to 3 significant figures.
...... cm2
(Total 3 marks)
[June 2011 Calc] 9.
Work out the total surface area of the triangular prism.
......
(Total 4 marks)
[June 2011 NonCalc] 25.
The diagram shows a solid cone and a solid hemisphere.
The cone has a base of radius x cm and a height of h cm.
The hemisphere has a base of radius x cm.
The surface area of the cone is equal to the surface area of the hemisphere.
Find an expression for h in terms of x.
......
(Total 4 marks)
[Nov 2010 Calc] 11. Here are four containers.
Water is poured into each container at a constant rate.
Here are four graphs.
The graphs show how the depth of the water in each container changes with time.
Match each graph with the correct container.
A and ...... B and ...... C and ......
D and......
(Total 2 marks)
[June 2010 Calc] 13. The diagram shows a solid prism.
(a) On the grid below, draw the front elevation of the prism from the direction of the arrow.
(2)
(b) On the grid below, draw the plan of the prism.
(2)
(Total 4 marks)
[June 2010 NonCalc] 20. (a) Here are some expressions.
a3b / a2( c+ b) / 4abc / ab + c3 / 4πc2The letters a, b, and c represent lengths.
π and 4 are numbers that have no dimension.
Two of the expressions could represent volumes.
Tick the boxes (? ) underneath these two expressions.
(2)
The volume of this cube is 8 m3.
(b) Change 8 m3 into cm3.
...... cm3
(2)
(Total 4 marks)