Question

the surface areas of two similar figures are 16 in squared and 25 in squared. if the volume of the larger figure is 500 in cubed what is the volume of the smaller figure?

Answer 1

1. Let
`A_1` and
`A_2` be the areas of 2 similar figures.

Similar figures have a scale factor k, (let k be >1, so k is the ratio of a distance in the larger figure to the corresponding distance in the smaller one)

The ratio of the area of the larger figure to the area of the smaller is
`k^(2)`

The ratio of the volume of the larger figure to the volume of the smaller is
`k^(3)`

2.
`(A_2)/(A_1)= (25)/(16)= ( 5^(2) )/( 4^(2) )= ( (5)/(4) )^(2)`

so k is 5/4

3.

`(V_2)/(V_1) = (500)/(V_1)= ( (5)/(4) )^(3)= (125)/(64)`


`(500)/(V_1)= (125)/(64)`


`V_1= (500*64)/(125)= 4*64=256` in cubed