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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? Choose level of difficulty 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