Lesson video

Hello, my name is Miss Parnham, and in this lesson, we will be solving surface area of cylinder problems. In this problem, the cylinder and cube have the same surface area.

So we can work out the surface area of the cylinder and then use that to find a missing dimension of the cube.

Right, what do we know about the cylinder? We know the height is 18 centimetres, the diameter is 24 centimetres, so the radius must be 12 centimetres, and the surface area of a cylinder is two PI R squared plus two PI RH Or if you like to fact arise that formula, two PI R multiplied by R plus H.

So, R in this example is 12 and H is 18.

So let's put those values in, and we can simplify this a little bit.

So two PI multiplied by 12 is 24 PI and 12 plus 18 is 30.

I know we can multiply 30 by 24, and that gives us 720 PI centimetres squared.

If you want to put this into your calculator and get an answer to three significant figures, this is 2,260 centimetres squared.

We're going to calculate with this, with the full answer in our calculators.

So the cube has a surface area of six X squared because every edge is the same length and we can call that X.

So one face is X squared and a cube has six faces.

Think about a dice, it has six faces.

So we know six X squared equals 2,260.

Remember, we're calculating with the accurate number.

Let's divide both sides by six and then let's square root that.

So X is 19.

4 centimetres 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.

In question one, we only actually needed the area of the curved face, which is a rectangle with dimensions nine PI around the top and 13 in height.

So we could probably do that mentally and get 117 PI before finding that accurately on our calculators.

I'm rounding to three significant figures.

Here's another 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.

Cubes have six faces, so the surface area is six X squared if X is the length of an edge.

Now don't confuse this with the volume formula, this is a quick example where the volume and surface area are actually the same value because in both cases, we would do six multiplied by six, multiplied by six, which is 216.

In this example, we know the surface area of a cylinder is 25.

2 metres squared.

And we know the diameter is 2.

9 metres, therefore, we know the radius is 1.

45 metres.

So the surface area of a cylinder is two PI R squared, plus two PI, R H.

We can rearrange this to isolate H.

So first we can subtract two PI R squared from both sides, and then if we divide that by two PI R that isolates H.

So let's use that now with the numbers that we have.

Keying this into the calculator, we see that the height is 1.

32 metres to three significant figures, all the time calculating with the accurate numbers in our calculator.

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.

Don't forget to have the diameter for the radius in part B.

For both examples, you do need to subtract two PI R squared and then divide by 13 PI in part A and 25 PI in part B for the heights.

Here's another 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.

It's very easy to forget about the flat rectangular face on a semicircular prism, particularly when you see the diagram drawn like this and it's hidden.

So this question does help by giving steps to work out each individual face.

The other way you could do it is, you could quickly sketch a net, and jot down the area of each face on that before summing them for the final surface area.

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