# A solid cube is cut into 8 cubes of equal volumes. Find the ratio of the total surface area of the given cube and that of 1 smaller cube.

When it is cut into 8 cubes of equal volumes, Volume of each cube will be a

^{3}/8

Let A be edge of each new cube.

A

^{3}= a

^{3}/8

A

^{3}= (a/2)

^{3}

A = a/2 ...(i)

Ratio of TSA of given cube to 1 smaller cube = 6a

^{2}/ 6A

^{2}

= a

^{2}/ (a/2)

^{2}

= a

^{2}/ (a

^{2}/4)

= 4a

^{2}/ a

^{2}

= 4/1

=

**4:1**