The volume of the cylinder is 42 cm ^ 3. Find the volume of a cylinder whose radius is 2 times larger.

The volume of a cylinder can be found by the formula:

V = P * R² * h;

where R is the radius of the cylinder, h is its height.

Then, according to the formula:

3.14 * R² * h = 42 cm³ is the volume of the first cylinder;

3.14 * (2 * R) ² * h = x cm³ is the volume of the second cylinder.

All other things being equal, if only the radius changes, we compose an equation by dividing both the right and left sides of the formulas:

(3.14 * R² * h) / 3.14 * (2 * R) ² * h = 42 / x;

3.14 * R² * h / 3.14 * 4 * R² * h = 42 / x;

x = 42 * 4;

x = 168 cm³.

Answer: 168 cm³.