Lateral surface area of a cone

**EMyk01** · Mar 7th 2011, 10:08 AM

I don't have the foggiest clue how to answer this question. Also, I don't have any intuition how to answer this without memorizing formulas. I've googled and found the formula for a lateral surface area of a cone: $L = \pi*r*\sqrt{r^2 + h^2}$

Now my test taking skills, I figured I can eliminate choices till I get a 50-50 guess.

My thought process knows there is 360 deg in a circle. There are nine - 40deg's in a circle. So that leaves me with B or D.
This thought process may be wrong: (And if I was in the test without the formulas in front of me). I know that a cone and a sphere both are curved. I know the surface area of a sphere has a radius squared. So I would presume I would square the 8" to get 64. So I would choose D, here.

But as I said earlier, I do not have any intuition on how to definitively answer this question. So how about it? Am I on the right track?

**earboth** · Mar 7th 2011, 10:21 AM

Originally Posted by EMyk01

I don't have the foggiest clue how to answer this question. Also, I don't have any intuition how to answer this without memorizing formulas. I've googled and found the formula for a lateral surface area of a cone: $L = \pi*r*\sqrt{r^2 + h^2}$

Now my test taking skills, I figured I can eliminate choices till I get a 50-50 guess.

My thought process knows there is 360 deg in a circle. There are nine - 40deg's in a circle. So that leaves me with B or D.
This thought process may be wrong: (And if I was in the test without the formulas in front of me). I know that a cone and a sphere both are curved. I know the surface area of a sphere has a radius squared. So I would presume I would square the 8" to get 64. So I would choose D, here.

But as I said earlier, I do not have any intuition on how to definitively answer this question. So how about it? Am I on the right track?

Your guessing skills are excellent

The lateral surface of a cone is a sector, that means a part of a circle. As you've said correctly you have $\dfrac{40}{360}$ of a circle with a radius of 8''.

The area of the complete circle is calculated by:

$a_{circle}=\pi r^2$

So in your case

$a_{sector}=\dfrac{40}{360} \cdot \pi \cdot 8^2$

Simplify the RHS and you'll get answer D. (But of course: Guessing is much faster)

**EMyk01** · Mar 7th 2011, 10:25 AM

And there is the intuition I was missing! It sounds silly, but I never realized that we were working with a section of a circle. :-p Wow, I am glad I understand it now instead of going into this feeling silly. Thanks.

Originally Posted by earboth

Your guessing skills are excellent

The lateral surface of a cone is a sector, that means a part of a circle. As you've said correctly you have $\dfrac{40}{360}$ of a circle with a radius of 8''.

The area of the complete circle is calculated by:

$a_{circle}=\pi r^2$

So in your case

$a_{sector}=\dfrac{40}{360} \cdot \pi \cdot 8^2$

Simplify the RHS and you'll get answer D. (But of course: Guessing is much faster)

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