# Lesson video

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Hi, I'm Ms Davis.

In this lesson, we're going to be calculating the volume and surface area of a cone.

This is a cone, we've been given the radius of the base and the height of the cone in total.

To calculate the volume of the cone is a multiply 1/3 by PI then by the radius squared and the height.

The radius is 10, and the height is 15.

This gives us an answer of 1,570 centimetres cubed round it to three significant figures.

Next we're going to calculate the surface area of the cone.

To find the area of the curved face of the cone, do PI multiplied by the radius, multiplied by the slant length.

We do not know what the slant length is, We're going to use Pythagoras' theorem to work it out.

This gives us a slant length of the square root of 325, which is 18.

028 centimetres.

We're going to use the square roots of 325 as it is more accurate.

You can then substitute these values into our formula to find, that the area of the curved face is 566.

359 centimetres squared.

Next we need to find the area of the base of the cone.

Base is PI r squared as it is a circle.

This gives us an answer of 314.

159 centimetres squared.

To calculate the total surface area of the cone, We need to add together the area of the curved face, and the area of the base.

This gives us 880.

5 centimetres squared.

This has been rounded to one decimal place.

Here's some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers, these have both been rounded to the nearest integer.

To find the slant length of this cone, You need the calculate the square root of seven squared, add 11 squared, which gives 13.

04 centimetres.

Here's a question for you to try.

Pause the video, to complete your task.

And resume once you're finished.

Here is the answer.

To calculate the volume of this cone, you need to work out 1/3 multiplied by PI, multiplied by 15 squared, multiplied by 20.

This gives an answer of 4,712.

4.

I have rounded this to the nearest 10, or three significant figures to give the answer of 4,710.

Here's a question for you to try.

Pause the video to complete your task, and resume once you are finished.

Here is the answer.

The radius of this cone is five centimetres.

To work up the slant length, you need to find the square root of 30 squared add five squared.

This gives 30.

4 centimetres.

My answer for the surface area has been rounded to the nearest integer.

That's all for this lesson.

Thanks for watching.