1. Choose level of difficulty 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?

2. Help Step 1: Find the volume of the top section (cylinder) The test tube consists of a cylinder and half a sphere (hemisphere) Draw the cylinder and mark on the dimensions (lengths) Volume of cylinder =  r 2 h 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? 9 3

3. 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  r 3 )/3 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? 3

4. 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. 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?

5. 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. 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?

6. Help Step 5: Work out the value for d Volume of cylinder =  r 2 h We know the volume in the cylinder and the radius so we can calculate h Now we can give the answer to d. 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? h 3 End of Problem Return to Menu End of Problem Return to Menu

7. Help Step 1: Find the volume of the top section (cylinder) The test tube consists of a cylinder and half a sphere (hemisphere) Draw the cylinder and mark on the dimensions (lengths) Volume of cylinder =  r 2 h 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? 9 3

8. 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  r 3 )/3 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? 3

9. 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. 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?

10. Help Step 4: Work out the value for d Volume of cylinder =  r 2 h We know the volume in the cylinder and the radius so we can calculate h Now we can give the answer to d. 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? h End of Problem Return to Menu End of Problem Return to Menu

11. Help Step 1: Split the section into two pieces and find their volumes Volume of cylinder =  r 2 h Volume of sphere = (4  r 3 )/3 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? 9 3 3

12. 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. 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?

13. Help Step 3: Work out the amount of liquid in the cylinder section 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?

14. Help Step 4: Work out the depth of water in the cylinder and then the value of d 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? h 3 End of Problem Return to Menu End of Problem Return to Menu

15. Help Step 1: Split the section into two pieces and find their volumes Volume of cylinder =  r 2 h Volume of sphere = (4  r 3 )/3 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?

16. Help Step 2: Work out the amount of liquid in the cylinder section 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?

17. Help Step 3: Work out the value for d 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? h End of Problem Return to Menu End of Problem Return to Menu

18. End of Problem Return to Menu End of Problem Return to Menu 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 =  r 2 h Volume of sphere = (4  r 3 )/3