Question

The ratio between the areas of two similar prisms is 4:9. If the mass of the smaller prism is 48 kilograms, what is the mass of the larger prism?

Answer 1

The mass of larger prism is `162` killograms. [Ans]

Explanation:

Mass is related to volume , Mass = Volume multiplied by density.

The ratio of area (2 dimension) of two similar prisms is `4:9`

So the ratio of l/b/h (1 dimension) of two similar prisms is

`sqrt(4): sqrt (9) or 2:3` and the ratio of volume (3 dimension) of

the similar prisms is `2^3:3^3 or 8:27`

Hence the ratio of masses of the similar prisms is `8:27`.

The mass of smaller prism is `48` killograms.

Therefore the mass of larger prism is `27/8*48= 162` killograms. [Ans]