165k views
3 votes
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.

User Lepton
by
7.6k points

2 Answers

2 votes

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

User Doogle
by
8.4k points
4 votes

Answer:

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.

User SuperZhen
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories