Question

Amanda used 24 grams of paint to paint a wooden cube. When it dried, she cut the cube into 8 equal cubes. How many more grams of paint does Amanda need to paint the unpainted surfaces of the 8 cubes?

Answer 1

Amanda will need 6 grams of paint to paint the unpainted surfaces of the 8 cubes.

Step-by-step explanation:

To find out how many more grams of paint Amanda needs to paint the unpainted surfaces of the 8 cubes, we first need to calculate the total surface area of one cube. Since all sides of a cube are equal, we can find the surface area by multiplying the length of one side by itself, and then multiplying that result by 6 (since there are 6 faces on a cube).

Let's assume the length of one side of the original cube is 'x'. So the surface area of one cube is 6 * (x * x) = 6x^2.

Next, let's calculate the surface area of the 8 smaller cubes. Since each side length is half of the original cube's side length, the surface area of each smaller cube is -

= 6 * ((x/2) * (x/2))

= 6 * (x^2/4)

= 3/2 * x^2.

Now, let's find the ratio of the surface area of the smaller cubes to the surface area of the original cube: (3/2 * x^2) / (6x^2) = (1/4).

Therefore, the surface area of the 8 smaller cubes is 1/4 times the surface area of the original cube. Since the amount of paint needed is proportional to the surface area,

Amanda will need 1/4 times the amount of paint she used for the original cube. So she will need 1/4 * 24 grams = 6 grams of paint to paint the unpainted surfaces of the 8 cubes.

Answer 2

Amanda needs 72 grams of paint

Step-by-step explanation:

Notice that she already painted one face of each cube, that is, 8 faces in total, and she used 24 grams for that.

Now, there remain 3 faces per cube to be painted, which means there are 24 faces.

Then, we use the rule of three, if she used 24 grams of paint for 8 faces, how much grams of paint she would need to paint 24 faces?

`24 * (24)/(8)= 72 \ grams`

Therefore, Amanda needs 72 grams of paint for the unpainted surfaces.