Lesson video

Hello, my name is Miss Parnham, and in this lesson, we will be solving volume of a cylinder problems. In this first example, we have a cylinder and a semicircular prism, or half cylinder, and Eva thinks that these have the same volume.

Let's investigate.

So we have a height of 22, a diameter of 10 and therefore a radius of five centimetres on our cylinder.

The formula for the volume of a cylinder is V equals Pi R squared, H.

Let's substitute five in for R and 22 in for H.

Now we know that five squared is 25, and multiplying them all together, that's 550 Pi centimetres cubed.

Now, let's look at the semicircular prism.

We have a height of 22, a diameter of 20, and therefore a radius of 10 centimetres.

Now the formula for the volume of this shape is a half Pi R squared H, so let's substitute 10 in for R and 22 in for H.

We all know that 10 squared is a hundred.

And this gives us an answer of 1,100 Pi centimetres cubed.

So no, Eva is not right.

In actual fact, that semicircular prism is twice the volume of the cylinder.

In this next example, we know the volume of the cylinder, and we're being asked to find out the height.

So we have a diameter of 3.

2, which means we have a radius of 1.

6 metres.

And the formula for the volume of a cylinder is Pi R squared H, let's rearrange this so that we can divide the volume by Pi R squared, and this will leave us with H.

Tapping this into the calculator, to three significant figures, we should find that this is 1.

70 metres.

Here, we've got another example.

This time, yes, we know the volume, but now we know the height and want to find the radius.

So we still use exactly the same formula, but we rearrange it to divide the volume by the height times Pi, that will leave us with the radius squared.

And that's equal to 17.

5.

We need to square root 17.

5 to find the radius and that is 4.

18 millimetres to three significant figures.

Here are some questions for you to try.

Pause the video to complete the task, and then restart the video when you're finished.

Here are the answers.

You had a couple of options with question one.

You could work out the volume of a whole cylinder with radius 12.

5 and height 37 centimetres, and then just divide by two for your answer.

Alternatively, you could calculate the area of the semicircle by squaring 12.

5, multiplying by Pi, and then dividing by two before going on to multiply it by 37 for the final answer.

Either way you would get 9,080 centimetres cubed to three significant figures.

Here we have some juice in a carton, which is a cuboid shape.

So we can work out the volume of the juice, 'cause it's filled right to the brim, by multiplying the length, by the weight, by the height.

And that gives us 1,870,000 millimetres cubed.

So this is going to get poured into the cylindrical jug which has a diameter of 120 millimetres, therefore it's got a radius of 60 millimetres.

And if we divide the volume of juice by Pi R squared, that will give us the height.

Pop that into your calculator and to three significant figures, that is 165 millimetres.

But the question is asking us, how far below the top of the jug will the juice be? So if the jug is 200 millimetres tall, then we just need the difference between that and 165.

So to three significant figures, this is 35 millimetres from the top.

Here's a question for you to try.

Pause the video to complete the task, and then restart the video when you're finished.

Here are the answers.

Patsy is essentially calculating the height, given the volume.

So we have rounded answers written next to the questions here, but all the time we are working with fully accurate answers in the calculator.

So when we subtract 70 from 311, we get 241.

We will then have to multiply that by a thousand in order to convert litres back into centimetres cubed.

And then if we divide by the cross section of 900 Pi, we can see the height of the oil will be 85 centimetres to the nearest centimetre.

That's all for this lesson, thank you for watching.