If the largest sphere is carved out of a solid cube of side 21 cm, then the diameter of the sphere is equal to the edge length of the cube, which is 21 cm.
The volume of a sphere is given by the formula:
V = (4/3)πr^3
where r is the radius of the sphere.
Since the diameter of the sphere is 21 cm, the radius is half of that, or 10.5 cm. Substituting this value into the formula for the volume of a sphere, we get:
V = (4/3)π(10.5)^3
V = (4/3)π(1157.625)
V ≈ 6468.19 cubic centimeters
Therefore, the volume of the largest sphere that can be carved out of the cube with side 21 cm is approximately 6468.19 cubic centimeters
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Step-by-step explanation:
If the largest sphere is carved out of a solid cube of side 21 cm, then the diameter of the sphere is equal to the edge length of the cube, which is 21 cm.
The volume of a sphere is given by the formula:
V = (4/3)πr^3
where r is the radius of the sphere.
Since the diameter of the sphere is 21 cm, the radius is half of that, or 10.5 cm. Substituting this value into the formula for the volume of a sphere, we get:
V = (4/3)π(10.5)^3
V = (4/3)π(1157.625)
V ≈ 6468.19 cubic centimeters
Therefore, the volume of the largest sphere that can be carved out of the cube with side 21 cm is approximately 6468.19 cubic centimeters