 Hi in this video we are going to look at general formula for volume lateral surface area and total surface area for any even 3d solid and we will consider that a general 3d solid. So what we usually have when we have a solid is that we have a bottom surface area and if we pull it upwards and imagine while we pull it there is more matter that is created and the solid is created. So there is some top surface area and the bottom surface area like this which is equal and then there is this third dimension which is height to this solid which we can represent like this and I get a 3d solid. Now how do we find volume lateral surface area and total surface area of such solids? Let's see. So when we talk about volume we first need to find out this surface area of the bottom surface of the solid. So we need the base surface area and then we will multiply this area by the height of the solid times the height. Now in this case we can see that the base is triangular and in that case to find the base surface area we will have to apply the area of triangle and this base could be of any shape this could be circular this could be rectangular and with different changing solids this base surface area would keep on changing. Now what about lateral surface area? Now to find the lateral surface area what we need to look at is the perimeter of the base first and once we find the perimeter of this base then we extend that perimeter for the given height. So each of the sides when pulled above with the given height it gives us that particular surface area and each side contributing to the respective surface area gives us the total lateral surface area. So let's say lateral surface area is perimeter times the height. What about the total surface area? Total surface area is basically when once we add the top and bottom surface areas into the lateral surface areas and we already have seen that this top surface area and the bottom surface area are equal in the solid that we are considering. So total surface area will be equal to the lateral surface area I'll just write SA plus two times the base surface area so two times base surface area. Now let's just quickly take an example to solve for volume lateral surface area and total surface area. We will keep the same solid here now let us say the sides of the triangular surface of the given solid are 6 centimeter and 8 centimeter and those sides meet at the right angle. Now in order to find the volume of it volume will be given by the surface area of the base which is also triangular and so we will apply area of triangle formula half times base which is 6 times 8 for the triangle times the height of the solid and height of the solid is given as 20 centimeters and therefore this comes out to be 480 centimeter cube. What about lateral surface area? In this case lateral surface area will be the perimeter of the triangular base times the height. How can we find the perimeter? We already know two sides of the base third side can be found using Pythagoras theorem let's say the third side is L and in this case L square will be equal to 6 square plus 8 square and L will be square root of 100 and therefore L will be 10. So the third side is 10 centimeter. So the perimeter of this solid is 8 plus 6 plus 10 which is 24 centimeters times the height and height is 20 centimeter. This gives us the lateral surface area to be equal to 480 centimeter square. What about the total surface area? Total surface area will be the lateral surface area plus twice the base surface area or twice the top surface area. So twice of the area of the given triangle which is half times 6 times 8, 2 and half cancel out each other and then we get 48 plus 480 as the total surface area and the answer here is 528 centimeter square. Note the units for volume we have centimeter cube and for surface areas we have centimeter square and this is how in general we can find volume lateral surface area or total surface area of any given solid.