Question 1151760
One dimensional measurements (side lengths, perimeters, etc.) are in the ratio {{{a:b}}}.

Two dimensional measurements (area, surface area, etc.) are in the ratio of {{{a^2:b^2}}}

Three dimensional measurements (volume) are in the ratio of {{{a^3:b^3}}}



The ratio of the smaller area to the larger area is {{{147/3675=1/25}}}

then. the ratio of the height of the smaller cone and height of the larger cone
 ({{{80cm}}} )is 

{{{h/80=sqrt(1/25)=1/5}}} => {{{h=16cm}}}


so, ratio of the heights is {{{h[s]/h[l]=1/5}}}


then, volumes are in the ratio of 

{{{a^3/b^3=(1/5)^3}}}

{{{a^3/b^3=1/125}}}

{{{a^3/b^3=0.008}}}


using formula for the area of a smaller cone, we calculate radius: 

{{{A=  pi*r(r + sqrt(r^2 + 16^2))}}}

{{{147=  3.14*r(r + sqrt(r^2 +16^2))}}}

{{{r=2.5cm}}}

using formula for the area of a larger cone, we calculate radius:

{{{A =  pi*r(r + sqrt(r^2 + h^2))}}}

{{{3675=  pi*r(r + sqrt(r^2 + 80^2))}}}

{{{r=12.5cm}}}


the volume of a smaller cone is: 

{{{V = (1/3)pi*r^2*h}}}=>{{{V = (1/3)pi*(2.5)^2*16}}}=>{{{highlight(V=104.72cm^3)}}}

the volume of a larger cone is: 

{{{V = (1/3)pi*r^2*h}}}=>{{{V = (1/3)pi*(12.5)^2*80=13089.97cm^3}}} 


check the ratio:

{{{104.72/13089.97 =0.008}}}