Question

Imagine that you have gelatin cut into three cubes: the length of a side of cube A is a , the side of cube B is double the side of A , and the side of cube C is three times the side of A.

Determine the volumes of the cubes.

Express your answers in terms of a separated by commas.

Determine the surface areas of the cubes.

Express your answers in terms of a separated by commas.

Determine the cross-sectional areas of the cubes.

Express your answers in terms of a separated by commas.

Determine the masses of the cubes in terms of the density of gelatin ? .

Express your answers in terms of a and ? separated by commas.

Answer 1

Side of 1^st cube = a

Side of 2^nd cube=2a

Side of 3^rd cube = 3a

1. Volume of the cubes= side³

Volume of the cubes = a³ , 8a³ , 27a³

1. Surface area of cube = 6*(side²)

Surface areaof cube = 6a² , 24a² , 54a²

1. Cross sectional areas of the cubes = side * side

                      Cross sectional areas of the cubes = a² , 4a² , 9a²

1. masses of the cubes in terms of the density of gelatin:

density = mass/vol.

mass = density* vol.

let density = ?

masses of the cubes in terms of the density: = ?a³ , ? 8a³ , ?27a³