SOLUTION: I have a quiz tomorrow, and I don't quite understand the "ratio" thing. Can you help explain how to do this problem? Thanks. The ratio of corresponding linear measures of two si

Algebra ->  Volume -> SOLUTION: I have a quiz tomorrow, and I don't quite understand the "ratio" thing. Can you help explain how to do this problem? Thanks. The ratio of corresponding linear measures of two si      Log On


   

Question 1074830: I have a quiz tomorrow, and I don't quite understand the "ratio" thing. Can you help explain how to do this problem? Thanks.
The ratio of corresponding linear measures of two similar cones is 3 to 4. The smaller cone has a volume of about 18 inches. Find the volume of of the larger cone, and round the answer to the nearest tenth, if necessary.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
That ratio means that if radius and height for the smaller cone is r and h, then for the larger cone, they are (4/3)r and (4/3)h.

VOLUME, SMALL CONE
%281%2F3%29h%2Api%2Ar%5E2=18, cubic inches

%281%2F3%29pi%2A%28hr%5E2%29=18

VOLUME, LARGE CONE
%281%2F3%29%284%2F3%29h%2Api%2A%28%284%2F3%29r%29%5E2=V

%281%2F3%29pi%2A%28%284%2F3%29h%29%2A%284%2F3%29%5E2%2Ar%5E2=V

%281%2F3%29pi%2Ahighlight_green%28%284%2F3%29%5E3%29%2Ahr%5E2=V


To go from the small cone volume to the large cone volume, multiply the small cone's volume by highlight_green%28%284%2F3%29%5E3%29.
V=18%2A%284%2F3%29%5E3