Question

If a cube with the length of the side of 4 cm is cut into smaller cubes with the length of the side of 1 cm, then what is the percentage increase in the surface area of the resulting cubes?

Answer 1

300 %

Explanation:

Length of the larger cube =4 cm

So volume
`V=side^3=4^3=64cm^3`

Length of the smaller cube = 1 cm

Volume of the smaller cube
`V=side^3=1^3=1cm^3`

So total number of smaller cube
`=(64)/(1)=64`

Surface area of the larger cube
`A=6* side^2=6* 4^2=144cm^2`

Surface area of the 64 smaller cube
`A=64* 6* side^2=64* 6* 1^2=384cm^2`

So percentage increase in surface area
`=(384-96)/(96)* 100=300` %