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ACT Math 2.5 Plane Geometry 463 Views


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ACT Math Plane Geometry Drill 2, Problem 5. What is the surface area of a rigid circular cone with diameter = 10 and height = 12?

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Transcript

00:02

Here's your shmoop du jour.

00:04

What is the surface area of a rigid circular cone with diameter = 10 and height = 12?

00:12

And here are the potential answers...

00:15

Okay, it's yet another formula trivia contest.

00:19

So the formula is....

00:21

surface area equals pi times r times the square root of the quantity radius squared plus height squared.

00:27

Well, they give us the height. Now we need the diameter to tell us what the radius is;

00:32

...and in a circle, here is the diameter -- the radius is just half of it. So if diameter is 10

00:38

half is 5.

00:41

Now just plug in the numbers.

00:43

It's pi times 5 times the square root quantity of 5 squared plus 12 squared which simplifies to

00:49

5 pi times the square root quantity 25 plus 144 or 169 -- and ooh magic number --

00:58

169 should trigger a bell in your head.

01:02

It is 13 squared.

01:04

So we have 5 times pi times 13 -- 5 times 13 is 65 so the answer is 65 pi.

01:11

Answer D.

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