Final answer:
The volume of the largest sphere that can fit inside a cube with a side length of 1.4 cm is approximately 1.436 cubic centimeters (cm³), using the formula V = (4/3)πr³ with r = 0.7 cm.
Step-by-step explanation:
To find the volume of the largest sphere that can fit inside a cube, we need to first understand that the sphere's diameter will be the same as the length of a side of the cube. Given that the side of the cube is 1.4 cm, this will also be the diameter of the sphere, making the radius of the sphere half of that length, which is 0.7 cm.
Using the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume and r is the radius, we can calculate the volume:
V = (4/3)π(0.7 cm)³ ≈ (4/3)π(0.343 cm³) ≈ 1.436 cm³
Therefore, the volume of the largest sphere that can be taken out of the cube is approximately 1.436 cubic centimeters (cm³).