Question

A solid aluminum cube has sides each of length L . A second cube of the same material has sides four times the length of the first cube; i.e., 4 L . Compared to the first cube, the total surface area of the second cube is 1. twenty-seven times the first cube. 2. sixteen times the first cube. 3. sixty-four times the first cube. 4. eight times the first cube. 5. twenty-four times the first cube. 6. two times the first cube

Answer 1

Answer:

Option (2) : Sixteen times the first cube

Explanation:

$Surface \: Area \: of \: Cube = 6 {a}^{2}$

$\frac{T.S.A \: of \: larger \: cube}{T.S.A \: of \: smaller \: cube} = \frac{6 \times 16 {l}^{2} }{6 \times {l}^{2} } = 16$

Answer 2

When the linear dimensions of a solid are multiplied by ' R ', the surface area of all or any part of it increases by R² , and the volume of all or any part of it increases by R³ .

If the sides of the second cube are 4 times the sides of the first one, then the second cube has (4²) = sixteen times the surface area of the first one (2), and it has (4³) = 64 times the volume of the first one.