SOLUTION: Hello, I have two Similar cones Large and small. Large cone is 9cm radius 15 cm slant height. The small cone has a lateral area of 60 pi. How do I find the volume of the small

Question 1083682: Hello, I have two Similar cones Large and small. Large cone is 9cm radius 15 cm slant height. The small cone has a lateral area of 60 pi.
How do I find the volume of the small cone?
Found 2 solutions by MathLover1, addingup:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Large cone is and slant height
small cone has a lateral area of
The lateral area of a cone is
where is the radius and is the slant height

since cones similar, radii and slant heights are proportional:

-> slant height of a small cone

-> radius of a small cone

now we can find a volume:
where is base and height of the cone
base is a circle: area is
so,
we will find height using Pythagorean theorem:
-> ->->->

Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
radius: r
length of the slant side: l
height: h
-------------
height: h = sqrt(l^2-r^2)
your large cone:
h = sqrt(15^2-9^2) = 12
------------------
Area of the base : Pi*r^2
Lateral area . . : Pi*r*l (large cone: Pi*9*15 = Pi*135 = 424.12)
Area of the cone: Pi*r^2+Pi*r*l
your large cone:
area = (Pi*9^2)+(Pi*9*15) = 254.47+424.12 = 678.58 is the total area of the large cone
----------
Volume of the cone: (Pi*r^2*h)/3 = (Pi*81*12)/3 = 1,017.88
---------------------
Your small cone has a lateral area of 60*Pi = 188.50 and from the formula we know that 60 = r*l. But here I get stuck. How are your cones similar? Do they have the same lateral area ratio, 424.12:188.50?
I somehow don't think so, I think it's something else. Do they have the same slant height? Or the same height? or the same radius?
RELATED QUESTIONS
The Ice Cream Depot has two sizes of waffle cones. The small cone has a volume of... (answered by josgarithmetic)
Two similar cones have heights of 3 feet and 12 feet. What is the ratio of the volue of... (answered by KMST)
What is the slant height of a cone that has a Lateral surface area of 285 sq cm and a... (answered by macston)
A cone has a slant height of 9cm and curved surface 65πcm^2 find: (a) The base radius... (answered by mananth)
The truncated right circular cone below has a large base radius $8$ cm and a small base... (answered by ikleyn)
Please help me solve this : two similar cones have corresponding slant height of 8cm... (answered by Alan3354)
Two similar cones have a combined volume of 400 in.^3 and the larger cone holds 80 in^3... (answered by Theo)
There are two cones. one smaller than the other. Small cone is 13.5m by 30m. large cone... (answered by Alan3354)
The area of the lateral surface of a cone is πrl, where l is the slant height. Find the... (answered by ikleyn)