Question

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

the figure shows the liquid filter as an open cone with a slant height of 12 cm and radius of 9 cm

If a similar cone has a slant height of 16 cm, what is its lateral area?

192π cm2

384π cm2

208π cm2

256π cm2

Answer 1

what formula do i use?

Answer 2

First we need to find the lateral surface area of this given cone, we do so using the formula

LSA = pi*r*s

where r is the radius and s is the slant height

So the lateral surface area in this case is

LSA = pi*r*s

LSA = pi*9*12

LSA = 108pi

Answer 3

You use the formula LSA = pi*r*s, one sec

Answer 4

oo ok!

Answer 5

Since the figures are similar, we can use this idea.


Notice how the slant height goes from 12 to 16. So we multiply 12 by some number to get 16.

So 12x = 16 ---> x = 16/12 = 4/3

So we multiply 12 by 4/3 to get 16.

Do the same with the radius to get

9*(4/3) = 36/3 = 12

Therefore, the new radius of this larger cone is 12 cm

------------------------------

So the new lateral surface area is


LSA = pi*r*s

LSA = pi*12*16

LSA = 192pi

Answer 6

So if a similar cone has a slant height of 16 cm, then it's lateral area is 192π cm2

Answer 7

thank you hun:)

Answer 8

sure thing