1. Choose level of difficulty
Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
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2. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 1: Copy the trapezium shape of the pool and write on the measurements.

3. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 2: The pool is not filled to the top so you need to take the top bit away from the trapezium. Write down the measurements for the filled section

4. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 3: Work out the area of the trapezium. One method is to split the shape into two parts

5. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 4: Find the volume of the pool.
Note it is a prism with a trapezium cross section. 4m

6. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 5: Calculate how long it takes to fill up a pool with this volume of water.

7. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 6: Calculate the time by which the pool will be full.
End of Problem
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8. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 1: Copy the trapezium shape of the pool and write on the measurements.

9. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 2: The pool is not filled to the top so you need to take the top bit away from the trapezium. Write down the measurements for the filled section

10. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 3: Work out the area of the trapezium. One method is to split the shape into two parts

11. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 4: Find the volume of the pool.
Note it is a prism with a trapezium cross section. 4m

12. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 5: Calculate how long it takes to fill up a pool with this volume of water.

13. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 6: Calculate the time by which the pool will be full.
End of Problem
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14. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Hint
Step 1: Draw a sketch

15. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Hint
Step 2: The pool is not filled to the top.

16. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Hint
Step 3: Work out the area of the trapezium.

17. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Help
Step 4: Find the volume of the pool.

18. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?

19. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
End of Problem
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20. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Hint
Step 1: Sketch the trapezium as high as the water level

21. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Hint
Step 2: Find the volume of the pool.
Note it is a prism with a trapezium cross section.

22. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Hint
Step 3: Calculate how long it takes to fill up a pool and the time it is completed.
End of Problem
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23. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Hint
Step 1: Find the volume of the water pool.

24. Volume of Prisms - Pool
The swimming pool has two identical sides in the shape of a trapezium. All other sides are rectangular.
The length of the pool is 12 m.
The width of the pool is 4 m.
The depth of the pool is 2.1 m at the deep end and 1.1 m at the shallow end.
Rafa fills the pool up with water from a hosepipe.
The surface of the water is to be 10 cm from the top of the pool.
Rafa turns on the hosepipe at on Monday and water fills at a rate of 200 ml per second.
When the pool is full, Rafa turns off the tap. At what time will this be?
Hint
Step 2: Calculate how long it takes to fill up a pool and the time it will be filled.
End of Problem
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