Question

A solid cube cut into 125 identical cubes by what percentage the lateral surface area increases​

Answer 1

Answer:

L.S.A decreased by 96%

Step-by-step explanation:

Let the initial side length of cube = a

Let the side length of cut cubes = b

Then

Volume of 1st cube = 125× volume of cut cube

→ a³ = 125b³ {Volume of cube = (side length)³}

→ a = 5b

L.S.A of cube = 4(side length)²

→ L.S.A of 1st cube = 4a² -eqn.1

→ L.S.A of cut cube = 4b²

As, a = 5b, substitute in eqn.1

L.S.A (1) = 100b²

L.S.A (2) = 4b²

%L.S.A↓ = ((100-4)b²/100b²)×100 = 96%