Volume 2 - Suffolk Maths

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 Return to Menu

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 Return to Menu

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 Return to Menu

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 Return to Menu

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 Return to Menu