 Let's say we wanted to find the surface area of a cone with radius is equal to 21 centimeters height of the cone has 28 centimeters and The slanted height Would be unknown. We know that the surface area or the curved surface area of the cone is given by pi R L and if we don't know L what we can use in this place is pi times R and then use The formula for L which is square root of R square plus H square and we will be happy to use this formula and plug in values to find Out the third surface area. So this is radius, which is 21 centimeters. This is the height of the cone which is 28 centimeters and And this is the slanted height. We don't know the measure of this Now, let's see how we can find out the surface area here. So CSA is Equal to pi. So we'll let's use the value 22 over 7 for pi Times R, which is the radius and it is given as 21 centimeters. Then we will write the square root of 21 square plus H square, which is 28 centimeter square and this is going to give us the curved surface area for the cone So if we want to solve this we can write 21 as three times seven and Then inside the square root. We have 441 plus 784 441 is the square of 21 and 784 is the square of 28 because we have written 21 as three times seven We can cancel these sevens out and we are left with 22 Let's just put equal sign because all these are equal. So 22 times 3 times the square root of the sum that we get here and the sum is 1225 we find that the curved surface area here is 22 times 3 times Square root of 1225, which is 35 and once we solve this I should have I should have written centimeters here Here and here as well because this is a length which has the unit of centimeters and This is also centimeter. So let's combine centimeter square here and here because I am multiplying these two centimeters so the unit is going to be centimeter square and Final value that we get is 66 times 35 centimeter square Which is nothing but 110 centimeter square and this is how we can find out the curved surface area for the given cone Now what if we wanted the total surface area instead of the curved surface area? We know that the TSA or total surface area is basically curved surface area plus Pi r squared my pirate squared is because We want to add the area of the disk circular disk. That's it at the bottom We can actually compute pi r square and then add it to 23 and 20 310 But I want to use the formula again. So CSA formula is basically pi r l plus pi r squared So the CSA formula is pi r l plus I want to add pi r squared to get TSA and this is nothing but pi r times r plus l I Know that by 22 by 7 times r r is 21 and what is r plus l r is 21 I already know l is this value because I have computed the square root of 1225 which was basically square root of r square r square plus h square and therefore you can safely say that l is equal to 35 from this all computation. So I can just write 35 here and then r plus l is basically 35 plus 21 which is 56 and Now let's again simplify 21 by 7 which is going to be 3. So I can write TSA is equal to 22 times the simplification of 21 and 7 which is 3 and then 56 and This gives me the value as 3696 centimeters square and this is the total surface area. I have already calculated the curved surface area for the cone which is 2310 centimeters square and After the after adding the surface area for the circular disc at the bottom the total surface area of the cone becomes 3696 centimeters square