Question

This is the problem ​

Answer 1

192 mm³

Explanation:

given 2 similar figures with ratio of sides = a : b , then

ratio of areas = a² : b²

ratio of volumes = a³ : b³

here ratio of areas

= 80 : 245 ( divide both parts by 5 )

= 16 : 49

then ratio of sides =
`√(16)` :
`√(49)` = 4 : 7 and

ratio of volumes = 4³ : 7³ = 64 : 343

let x be the volume of the smaller prism then by proportion

`(ratio)/(volume)` :
`(343)/(1029)` =
`(64)/(x)` ( cross- multiply )

343x = 64 × 1029 = 65856 ( divide both sides by 343 )

x = 192

that is the volume of the smaller prism = 192 mm³