Question

Find the slant height for a right circular cone with a radius of 3 and a height of 5.


4
√(31)
√(34)

Answer 1

Okay. So the easiest way to go about this one is to draw a picture, so why don't we. One sec.

Answer 2

So, looking at this picture we can see the image of a triangle forming.

Answer 3

From there, if you know Pythagorean's theorem, you should be able to find the slant height
if a= 5 and b=3

and a^2 + b^2 = c^2

Answer 4

Then c (the slant height) is going to be sqrt( a^2 +b^2)

sqrt( 9+25)

sqrt(34)

Answer 5

So it will be the third option.

Answer 6

Does that make sense? Any questions?

Answer 7

yes is does! Thank you!

Answer 8

No problem. If you're ever confused on a problem about shapes, it always helps to draw a picture.

Answer 9

It'll show things that aren't immediately easy to recognize (ie pythagorean's theorem in that problem).

Answer 10

Yeah. Thats the best thing to do!

Answer 11

can you help me on this question? A large dump truck will empty its full load of stone onto a small plot of land for storage. The rock forms a cone that is 9 feet tall. The truck holds 144 cubic feet of stone. What is the area of the circular base of the pile of stones?

Answer 12

Alright. So another good thing to do is to just throw some of your known formulas on the paper and see if any fit. Lets try the volume of a cone

Answer 13

If I remember correctly the volume of a cone is 1/3 pi r ^2 h yes?

Answer 14

yep!

Answer 15

Alright. So let's try plugging stuff in. We know the volume and the height of the cone, so we have the formula

144= (1/3)pi (r^2) 9

Answer 16

And since pi is just a number, we can figure out the radius of the cone by moving some of the numbers around.

Answer 17

And since the area of the base of a cone is just a circle (pi r^2) you'll be able to plug that r back in to that equation.

Answer 18

I can go through the numbers if you want, but if you see the process that should just be a little busy work

Answer 19

Just doing some of the work in my head it's looking like it's going to be about 45 pi?

Answer 20

give or take a few

Answer 21

okay . well, the answers are
12√2
18√2
27

Answer 22

Hm

Answer 23

im sorry wrong problem.

Answer 24

the answers are
48 square feet
square feet
16 square feet
square feet

Answer 25

oh okay

Answer 26

Forget the pi, it's actually going to be something like 45ft^2

Answer 27

Yeah 48 looks right

Answer 28

(144x3)/9

Answer 29

Since the pis cancel out and the square/squareroot cancel.

Answer 30

the second one is 48 / pi
the last one is sqrt48/pi

Answer 31

Again, you can go ahead and do the math if you want to double check. Pretty sure its 48ft^2.

Answer 32

144= (1/3)pi (r^2) 9

Answer 33

Find the r of that

Answer 34

and then plug it in to

pi(r)^2

Answer 35

And all that is is taking the volume of a cone, and plugging in some of the stuff you know (The cone's volume and its height).

Answer 36

after that its algebra.

Answer 37

I went ahead and went with the second suggest and got it wrong. but i passed the lesson.

Answer 38

Was the second one 48 square feet? If so you might want to check with your teacher.

Answer 39

Cause that may be wrong.

Answer 40

no it was 48/pi

Answer 41

Hmm Okay. Let's see.

Answer 42

Wait, was 48 over pi the answer you put in or the answer that was right?

Answer 43

the answer that I put in.

Answer 44

Ah. Answer should have been 48. Sorry about giving you the wrong answer at first. Messed up some of the algebra

Answer 45

Should be a lot easier on a test if you actually have pencil and paper to write stuff down =p

Answer 46

Any questions you got wrong earlier that you'd like clarification on?

Answer 47

ah. well thanks for working it out though.

Answer 48

no The one I missed I understand how to do it.

Answer 49

Alright. Good luck with future homework then. :)