Question

A solid cube is cut into 27 small cubes of equal volume. Find the ratio of the surface areas of the given cube and that of one small cube

Answer 1

Let the side of bigger cube be a its volume a^3 no. of smaler cubes = 27 their volume = a^3/27 each of smaller cube = (a^3/27)^1/3 = a/3. total surface area of bigger cube = 4×a^2=4a^2 total surface area of smaler cube=4(a/3)^2=4a^2

ratio of TSA of bigger cube to TSA of smaller cube = TSA of bigger cube/TSA of smaller cube =4a^2÷4a^2/9 = 9 : 1 HOPE IT HELPS