ʕᴥʔ Surface Area and Volume of a Cone - Formula and Example

Quickly master how to find the surface area and volume of a cone. Watch more lessons like this and try our practice at We just learned how to calculate the surface area and volume of pyramids and cylinders in the previous lessons. Now we will look at cones ? objects that have circle bases like cylinders and pointy tops like pyramids. Just like pyramids and cylinders there are formulas for surface area and volume of cones. We will also try out some questions on composite solids that consist of cones too. Hi so welcome to this question right here. Its a cone okay? Were trying to find the surface area and the volume. So before we start were going to always check the dimensions to see if theyre consistent with each other. We got the inch on the top and the feet on the bottom. So not good. So my suggestion is that you change the 0.75 feet into inches. That will be much better. So if you remember for every foot theres 12 inches. So were just going to take the 0.75 and times by 12 to get inches. So Im going to cross this one out right here. And inch would be I believe I have it written down here will be just 9 inch okay? So this part right here is just 9 inch okay? So now we can put things together but before we go ahead and calculate the surface area theres one more thing that were missing. Its the slanted side that were missing. So Im just going to draw a line down this way to represent the slanted side of the cone okay. Its called the S okay? We need that piece of information too for the later calculations. So as you can see you can get yourself a right triangle right here. We got the bottom piece which is 9 inch and we also got the center which is the height is the 20. So the slanted side which is the S is just going to be using by- Can be calculated by the Pythagorean Theorem. So we got the 9 inch and were going to square that and its going to be added to the 20 inch and were going to square that as well And the square root okay? So if you do the math correctly we get 21.9. So this is 21.9 inch. So once we have everything ready lets go ahead and calculate the surface area. So surface area of the cone we do have an equation for this. Its the Ïr2 Ïr2 plus the Ïrs. So thats why we need the slanted side okay? So lets go ahead and plug in the values that we have. The radius is the 9 inch. And square that plus the Ï and the 9 inch again. And times the slanted side which is 21.9. So heres my 21.9. And if you do the math correctly on your calculator youre going to get a nice number 875 okay? And thats with inch squared. That is the surface area of the entire thing. Now if youre wondering why do we have two pieces of information the Ïr2 is for the base of the cone. And the Ïrs is for the surface of the cone around it. So that is the final answer for the surface area. Now lets go ahead and calculate the volume. The volume for the cone we do have another equation for that. Its just a one third of the base area and were going to multiply by the height of the cone okay? So were going to go ahead put the one third back in there. Now the base of the cone is the circular part down here. So its a circle. So were going to use the Ïr2. So Im going to put a Ï we put a radius in. Its a 9 inch and going to square that and Im going to times the height which is the 20 okay? Not the slanted side its just the height of the cone. Its the 20 okay? So lets calculate the volume. We got 1696.5 and the unit is inch cubed. Okay so dont worry about it. So dont forget about it. So thats it. Thats your volume right there. Thanks for watching. Watch more step by step examples at Follow us YOUTUBE GOOGLE FACEBOOK TWITTER ,

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