A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?

48

To determine the weight of the larger cube, we need to understand the relationship between the weight and the dimensions of the metal block. Weight is directly proportional to the volume of an object.

The volume of a cube is calculated by multiplying the length of one side by itself twice. If the sides of the smaller cube are length "x", then its volume can be expressed as x^3.

Now, the weight of an object is directly proportional to its volume. So, if the weight of the smaller cube is 6 pounds, we can write the following equation:

Weight of smaller cube / Volume of smaller cube = Weight of larger cube / Volume of larger cube

Let's plug in the known values:

6 pounds / x^3 = Weight of larger cube / (2x)^3

Simplifying the equation:

6 pounds / x^3 = Weight of larger cube / 8x^3

Next, cross multiply:

Weight of larger cube = 6 pounds * 8x^3 / x^3

Simplifying further:

Weight of larger cube = 48 pounds

Therefore, the larger cube of the same metal will weigh 48 pounds if its sides are twice as long as the smaller cube.

If x^3 (volume) = 6 lbs,

then (2x)^3 = ?