Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
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Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 1:
Find the volume of
the top section
(cylinder)
The test tube consists of a
cylinder and half a sphere
(hemisphere)
9
Draw the cylinder and mark
on the dimensions (lengths)
Volume of cylinder = r2h
3
Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 2:
Calculate the volume
of the hemisphere.
Work out the volume of a
complete sphere and half the
answer.
Volume of sphere = (4 r3)/3
3
Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 3:
Work out the
volume filled in the
test tube.
Find the total volume of the
test tube and then find half of
that amount.
Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 4:
Work out the
amount of liquid in
the cylinder section
The amount in the cylinder
section of the test tube = the
amount of liquid – the amount
in the hemisphere.
Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 5:
Work out the value
for d
Volume of cylinder = r2h
We know the volume in the
cylinder and the radius so we
can calculate h
Now we can give the answer
to d.
h
3
End of Problem
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Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 1:
Find the volume of
the top section
(cylinder)
The test tube consists of a
cylinder and half a sphere
(hemisphere)
9
Draw the cylinder and mark
on the dimensions (lengths)
Volume of cylinder = r2h
3
Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 2:
Calculate the volume
of the hemisphere.
Work out the volume of a
complete sphere and half the
answer.
Volume of sphere = (4 r3)/3
3
Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 3:
Work out the
amount of liquid in
the cylinder section
The amount in the cylinder
section of the test tube = the
amount of liquid – the amount
in the hemisphere.
Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 4:
Work out the value
for d
Volume of cylinder = r2h
We know the volume in the
cylinder and the radius so we
can calculate h
Now we can give the answer
to d.
h
End of Problem
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Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 1:
Split the section into
two pieces and find
their volumes
Volume of cylinder = r2h
Volume of sphere = (4 r3)/3
9
3
3
Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 2:
Work out the
volume filled in the
test tube.
Find the total volume of the
test tube and then find half of
that amount.
Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 3:
Work out the
amount of liquid in
the cylinder section
Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 4:
Work out the depth
of water in the
cylinder and then
the value of d
h
3
End of Problem
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Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 1:
Split the section into
two pieces and find
their volumes
Volume of cylinder = r2h
Volume of sphere = (4 r3)/3
Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 2:
Work out the
amount of liquid in
the cylinder section
Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Step 3:
Work out the value
for d
h
End of Problem
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Probability
A test tube is shown below. It is
then filled to a depth d. If the test
tube is now exactly half filled what
is the value of d?
Help
Hint:
Volume of cylinder = r2h
Volume of sphere = (4 r3)/3
End of Problem
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