Each of 6 cubes has a volume of 64 cubic units. If the figure is reduced in size such that the volume of each new cube is 1/8 the volume of the original, what is the surface area of the 6 cubes after the decrease?

I came up with 96 sq units

Is this correct???

recall surface area and volume of cube is given by

SA = 6*s^2
V = s^3
where
s = length of a side
the volume becomes 1/8 of original so V' = 8 cubic units. thus,
8 = s^3
s = cuberoot(8)
s = 2 (new length)
the surface area of a cube of this length is
SA = 6*(2^2)
SA = 24 sq units (surface area of each cube)

now if there is a certain figure/shape given in the problem (for instance, the cubes are on top of each other, etc.) that we need to see and analyze (because it would really depend on the figure), the answer will not be equal to 24 sq units~

3 of the cubes are stacked

My choices were 48 sq ubits .
336 square units
96 square units
384 square units

if three cubes are stacked, the other three are stacked too, and they are put together, the figure i see is a rectangular prism of lengths 6, 4 and 2.

getting the SA of a rectangular prism,
SA = 2LW + 2LH + 2WH
SA = 2(6*4) + 2(6*2) + 2(4*2)
SA = 48 + 24 + 16
SA = 88 sq units.

now, if the figure i imagine is wrong, here's what you can do:
since you already know the new length of one cube, the area of one face is equal to 2x2 = 4 sq unit. now, count all the faces (of each cube that is EXPOSED) in the figure given, and multiply it by 4. you'll get the SA.

hope this helps~ :)

To find the surface area of the 6 new cubes after the reduction, we need to determine the side length of each new cube first.

Given that the volume of each new cube is 1/8 of the volume of the original cube, we can calculate the side length using the formula for the volume of a cube:

Volume = side length^3

Since the original volume is 64 cubic units, we have:

64 = side length^3

Taking the cube root of both sides, we find:

side length = ∛64 = 4

Now, we can calculate the surface area of one new cube. The surface area of a cube is given by the formula:

Surface Area = 6 * (side length)^2

Plugging in the side length of 4, we find:

Surface Area = 6 * (4)^2 = 6 * 16 = 96 square units

So, the surface area of the 6 new cubes after the reduction would be 96 square units.

Therefore, your answer of 96 square units is correct.