Question

If each edge of a cube is doubled,
(i) how many times will its surface area increase?
(ii) how many times will its volume increase?

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Answer 1

Answer:

i)4 ii)8

Step-by-step explanation:

As we know that the cube has 6 sides and each side represents the square.

And the area of square is (side)^2

Let the side length of the cube be a unit.

So the surface area (S.A) of the cube is = 6a^2 sq.unit

Volume of cube is = (side)^3

V = a^3

Now it is given that the cube is doubled

So now the edge of cube becomes 2a

New surface area of cube(S.A1)  is 6(2a)^2 = 24a^2 sq. unit

S.A1) =  4S.A)

i) Thus, the new surface area of cube is 4 times  the old surface area.

And the new volume of cube is = (2a)^3 = 8a^3

ii) Thus, the new volume of cube is 8 times the old volume.