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 09 00 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?
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.
Help
Step 1:
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 09 00 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?
Copy the trapezium
shape of the pool
and write on the
measurements.
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
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
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 09 00 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?
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Help
Step 3:
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 09 00 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?
Work out the area of
the trapezium. One
method is to split
the shape into two
parts
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Help
Step 4:
Find the volume of
the pool.
Note it is a prism with a
trapezium cross section.
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 09 00 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?
4m
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Help
Step 5:
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 09 00 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?
Calculate how long it
takes to fill up a pool
with this volume of
water.
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Help
Step 6:
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 09 00 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?
Calculate the time by
which the pool will
be full.
End of Problem
Return to Menu
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Help
Step 1:
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 09 00 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?
Copy the trapezium
shape of the pool
and write on the
measurements.
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
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
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 09 00 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?
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Help
Step 3:
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 09 00 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?
Work out the area of
the trapezium. One
method is to split
the shape into two
parts
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Help
Step 4:
Find the volume of
the pool.
Note it is a prism with a
trapezium cross section.
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 09 00 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?
4m
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Help
Step 5:
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 09 00 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?
Calculate how long it
takes to fill up a pool
with this volume of
water.
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Help
Step 6:
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 09 00 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?
Calculate the time by
which the pool will
be full.
End of Problem
Return to Menu
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Hint
Step 1:
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 09 00 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?
Draw a sketch
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Hint
Step 2:
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 09 00 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?
The pool is not filled
to the top.
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Hint
Step 3:
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 09 00 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?
Work out the area of
the trapezium.
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Help
Step 4:
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 09 00 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?
Find the volume of
the pool.
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 09 00 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?
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 09 00 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
Return to Menu
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Hint
Step 1:
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 09 00 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?
Sketch the
trapezium as high as
the water level
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Hint
Step 2:
Find the volume of
the pool.
Note it is a prism with a
trapezium cross section.
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 09 00 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?
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Hint
Step 3:
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 09 00 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?
Calculate how long it
takes to fill up a pool
and the time it is
completed.
End of Problem
Return to Menu
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Hint
Step 1:
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 09 00 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?
Find the volume of
the water pool.
Volume of Prisms - Pool
The swimming pool has two identical sides in the
shape of a trapezium. All other sides are rectangular.
Hint
Step 2:
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 09 00 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?
Calculate how long it
takes to fill up a pool
and the time it will
be filled.
End of Problem
Return to Menu