Surface area of a cone The lateral surface area of a cone of r...

Question

Surface area of a cone The lateral surface area of a cone of radius r and height h (the surface area excluding the base) is A = πr√r²+h².

b. Evaluate this derivative when r=30 and h=40.

Accepted Answer

Hello. In this video, we are going to be approaching the following surface area problem. So we are told that the total surface area of a cylinder with radius R and height H is given as A is equal to 2 R multiplied by R plus H. We want to calculate the value of the derivative DRDH if the area is equal to 500 pi, the radius is equal to 5, and the height is equal to 12. Now, in a previous video, we did complete the first part of this problem. We had determined what the derivative DRDH is if the area is equal to 500 pi. That derivative DRDH was equal to negative R divided by 2 R plus H. Since we have the derivative, when the area is equal to 500 pi, we now want to determine the value of the derivative when the radius is equal to 5, and the height is equal to 12. In order to do this, we will take the values of the radius and height and plug it into the derivative we had solved for. That will give us -5 divided by 2 multiplied by 5 plus 12. And all we need to do is just simplify the value. The denominator will simplify to be 10 + 12, which will be 22. That is going to give us -5 divided by 22, which is going to be the value of the derivative with the given values. And with that being said, the solution to this problem is going to be B. So, I hope this video helps you in understanding on how to approach this problem, and I will go ahead and see you all in the next video.

Surface area of a cone The lateral surface area of a cone of radius r and height h (the surface area excluding the base) is A = πr√r²+h².b. Evaluate this derivative when r=30 and h=40.

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Surface area of a cone The lateral surface area of a cone of radius r and height h (the surface area excluding the base) is A = πr√r²+h².
b. Evaluate this derivative when r=30 and h=40.