A right circular cylindrical metal rod, whose length equals its base radius, is melted and cast into several identical spherical balls, whose radius is half the base radius of the rod. How many such spherical balls are made?3 Mark For ReviewA) 3B) 4C) 6D) 8
Question
A right circular cylindrical metal rod, whose length equals its base radius, is melted and cast into several identical spherical balls, whose radius is half the base radius of the rod. How many such spherical balls are made?3 Mark For ReviewA) 3B) 4C) 6D) 8
Solution
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. In this case, the height equals the radius, so the volume of the cylinder is V = πr³.
The volume of a sphere is given by the formula V = 4/3πr³. In this case, the radius of the sphere is half the radius of the cylinder, so the volume of the sphere is V = 4/3π(r/2)³ = 4/3πr³/8 = πr³/6.
The number of spheres that can be made from the cylinder is the volume of the cylinder divided by the volume of one sphere, which is (πr³) / (πr³/6) = 6.
So, the answer is C) 6.
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