Question

what is the length of the radius of the LARGER cone(the LARGER cone has a slant height of 15) when the SMALLER cone has a radius of 8 and a slant height of 12ft ,please help.

Answer 1

Answer: 10 feet

Step-by-step explanation: Same answer, different explanation.

It says the cones are similar, so we can set up a proportion.

8/12 = x/15 (radius over slant height = radius over slant height)

and solve for x by using cross-products

12x = 120

x = 10

Answer 2

The radius of the larger cone is equal to 10 ft.

Explanation:

For the smaller cone, we have:

radius = r = 8 ft

slant height = l = 12 ft

slant angle = Ф = sine inverse(l/r)

= sine inverse(8/12)

Ф = 42°

Now

For larger cone, with same slant angle,

Slant height = 15 ft

Radius = r =?

r = l sin(Ф)

r = 15*sin(42°)

r = 15*0.669

r = 10 ft

Hence, the radius of a cone with slant height 15 ft and slant angle 42° would be equal to 10 feet.