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

Answer:

300 %

Step-by-step 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 $=\frac{64}{1}=64$

Surface area of the larger cube $A=6\times side^2=6\times 4^2=144cm^2$

Surface area of the 64 smaller cube $A=64\times 6\times side^2=64\times 6\times 1^2=384cm^2$

So percentage increase in surface area $=\frac{384-96}{96}\times 100=300$ %