Help?? (Don't ditch me like other have done)

A liquid filter shaped as a right circular cone is shown below.

If a similar cone has a slant height of 24 cm, what is its lateral area?

Question

Help?? (Don't ditch me like other have done)

A liquid filter shaped as a right circular cone is shown below.

If a similar cone has a slant height of 24 cm, what is its lateral area?

anonymous · Answer

attachment

anonymous · Answer

Lets us find the height first. Do you know how?

anonymous · Answer

why do we need the height we already have the slant height?

anonymous · Answer

In similar cones the height and radius are in proportion.

anonymous · Answer

then I guess I would not know the height..

anonymous · Answer

Use Pythagorean Theorem.

anonymous · Answer

the height would be 22?

anonymous · Answer

No.

anonymous · Answer

no dimmy... use the pythagorean theorem on this... solvefor h...
|dw:1338224704106:dw|

anonymous · Answer

5^2+20^2=h correct?

anonymous · Answer

No.

anonymous · Answer

then idk..

anonymous · Answer

you said use pythgoran theorem? Which is a^2+b^2=c^2 ??

anonymous · Answer

20 is the hypotenuse... so c=20.  solve for h. it is one of a or b in a^2+b^2=c^2

anonymous · Answer

so it's 15

anonymous · Answer

ok so i have figured out the height, now what?

anonymous · Answer

........

anonymous · Answer

I think $$S = \pi*r*l$$
S -area
$$\pi=3,14$$
r-radius = 5 
l- height = 20cm
S = 3,14 * 5*20 =314  
But I don't sure

anonymous · Answer

i got that too. But that is not one of the choices. The other two guys that were helping me ditched me (ofcourse).

anonymous · Answer

its Pie times r times 24 + pie times r squared

anonymous · Answer

well here are the answers: 
                72π cm2
		120π cm2
		144π cm2
		256π cm2
And i didn't get a match :/

pfenn1 · Answer

Okay.  The lateral area of a cone is given by$$A_L=\pi r L$$ where r is the radius of the cone and L is the slant height. Do you have the radius and slant height of the larger cone?

pfenn1 · Answer

Hello?  @DimDanny?

anonymous · Answer

pfenn1, r=5 http://assets.openstudy.com/updates/attachments/4fc3adbde4b0964abc864de1-dimdanny-1338224087203-help_image.gif

pfenn1 · Answer

@Palmo4ka, for the smaller cone it is 5, but @DimDanny needs to determine the lateral area of the larger cone.

pfenn1 · Answer

To determine the radius of the larger cone, we know that the cones are similar so therefor, the ratio of the slant heights equal the ratio of the radii $$\frac{20}{24}=\frac{5}{r}$$where r is the radius of the larger cone.

anonymous · Answer

Hence, r the large cone = 6