Geometry lateral area of a cone

The lateral area of a cone is L = πrl
π = 3.14 r = radius and, l = slant height
r = ½ of diameter 20
r = 10
l = 2.46
π(10)(2.46)
= 77.244 km^2
 
The slant height is not the same as the height. To find the slant height, use the Pythagorean theorem.
 
Correct. They gave you the (vertical) height h, not the slant height l. Look at the diagram for the formulas.
 
Why wouldn't you? (Well, I wouldn't use the word "perfect". What do you mean by that?)

But before you do that, you should check whether your work so far is correct. It isn't.

You don't need to ask about every step; just do it, show your work for the whole problem, and then ask. If I were tutoring you in person, I would ask you to do exactly that before I'd intervene, in part to give you a chance to learn how to check your own work step by step, rather than getting used to relying on someone else. The only way to learn the right combination of boldness and caution (trust yourself but verify your work) is to do whole problems on your own, and see where you tend to make mistakes.
 
Dr.Peterson said:
Why wouldn't you? (Well, I wouldn't use the word "perfect". What do you mean by that?)

But before you do that, you should check whether your work so far is correct. It isn't.

You don't need to ask about every step; just do it, show your work for the whole problem, and then ask. If I were tutoring you in person, I would ask you to do exactly that before I'd intervene, in part to give you a chance to learn how to check your own work step by step, rather than getting used to relying on someone else. The only way to learn the right combination of boldness and caution (trust yourself but verify your work) is to do whole problems on your own, and see where you tend to make mistakes.
Click to expand...
In one of the study guides I’m using for finding the slant height it says to find the perfect square root of each side. Sorry I’m unsure of my work
 
The term "perfect square" refers to a number that is the square of an integer (exactly). I don't know why someone would talk about "the perfect square root" when it is irrational, and you can only give an approximation.

To check, [MATH]l = \sqrt{10^2 + 2.46^2} = \sqrt{106.0516} = 10.298[/MATH]. I don't get 160.14 for the surface area, but something close to twice that. Please show your work, not just your answer.
 
I intentionally showed the correct work for that step, hoping you would see the mistake I had told you about (post #9). I suppose you didn't check your work as I told you to do.

But your new answer is correct, if you are required to use the approximation pi = 3.14. When you do that, however, you should not show six significant digits. The correct answer would be 323.
 
Dr.Peterson said:
I intentionally showed the correct work for that step, hoping you would see the mistake I had told you about (post #9). I suppose you didn't check your work as I told you to do.

But your new answer is correct, if you are required to use the approximation pi = 3.14. When you do that, however, you should not show six significant digits. The correct answer would be 323.
Click to expand...
How about rounded to the nearest hundredth?
 
If you are using a calculator, which I assume you are, then use the pi key, don't approximate pi to be 3.14.

The number of decimal places in your final answer is sometimes specified in the question or on the test as a whole. There's no hard and fast rule about the number of decimal places or sig figs in these sorts of questions.
 
The formula for lateral area of a cone is L = πrl
r = radius and, l = slant height
Radius = diameter/2
Radius = 20/2
Radius = 10
Use Pythagorean theorem to solve for slant height
l^2 = 10^2 + 2.46^2
l^2 = 100 + 6.05
l^2 = 106.05
Sqrt(106.05) = 10.29
l = 10.29 km
To solve for lateral area of cone
π(10)(10.29) = 323.106 km^2
L = 323.106 km^2
 
Another point. Don't round off too early, especially if you are giving that many decimal places.
Note that sqrt(106.05) doesn't equal 10.29 but equals 10.29813575.......... (you have a rounding error but that's not the point I want to make here).
By rounding off at this stage you are introducing an error (albeit a small one). By then multiplying by 10 *pi you are increasing that error.
Try not to round off until you get to the last step. Your calculator will allow you to multiply sqrt(106.05)^pi*10. Do that and you'll see the difference it makes to your final answer.
(Rachelmaddie, you are doing really well. Please take this as constructive criticism, just to finely tune your answers.):)
 
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