Geometry lateral area of a cone

Harry_the_cat said:
Yes I know that. But I always like the final line to actually answer the question as asked. That is, "the lateral area is ...."
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The formula for lateral area of a cone is L = πrl
π = 3.14 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) = 10.2980580694
l = 10.2980580694 km
To solve for lateral area of cone
π(10)(10.2980580694) = 323.52 km^2
L = 323.52 km^2
The lateral area is 323.52 km^2
 
If you've learned anything about significant figures, you should not be showing so many digits in your final answer; since 2.46 has three significant figures, that's how many you should use in the answer (though you would keep a couple more than that in intermediate steps, and I'd just do it all on the calculator anyway).

And I'd use a couple more digits of pi (actually, as many as the calculator internally uses), not just 3.14. It appears that you actually did use the pi button, so there was no need to state pi = 3.14. That's good.

On the whole, you have now shown your work in a way that adequately justifies your answer, and you have answered the question appropriately. (Your teacher, of course, is the judge of what is adequate, and has hopefully told your class what the expectations are, with examples.)
 
Dr.Peterson said:
If you've learned anything about significant figures, you should not be showing so many digits in your final answer; since 2.46 has three significant figures, that's how many you should use in the answer (though you would keep a couple more than that in intermediate steps, and I'd just do it all on the calculator anyway).

And I'd use a couple more digits of pi (actually, as many as the calculator internally uses), not just 3.14. It appears that you actually did use the pi button, so there was no need to state pi = 3.14. That's good.

On the whole, you have now shown your work in a way that adequately justifies your answer, and you have answered the question appropriately. (Your teacher, of course, is the judge of what is adequate, and has hopefully told your class what the expectations are, with examples.)
Click to expand...
I get a different approximation when I don’t use the whole decimal. How would I write it in this case?
Rounding to the nearest hundredths is fine in terms of the final answer but my trouble is writing out the sqrt(106.05)
 
Dr.Peterson said:
If you've learned anything about significant figures, you should not be showing so many digits in your final answer; since 2.46 has three significant figures, that's how many you should use in the answer (though you would keep a couple more than that in intermediate steps, and I'd just do it all on the calculator anyway).

And I'd use a couple more digits of pi (actually, as many as the calculator internally uses), not just 3.14. It appears that you actually did use the pi button, so there was no need to state pi = 3.14. That's good.

On the whole, you have now shown your work in a way that adequately justifies your answer, and you have answered the question appropriately. (Your teacher, of course, is the judge of what is adequate, and has hopefully told your class what the expectations are, with examples.)
Click to expand...
I’ve rounded to 323.5 km^2
 
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