Question : How many metallic spheres, each of diameter 6 cm can be melted to mould into a solid cylinder of diameter 8 cm and height of 18 cm?
Option 1: 6
Option 2: 12
Option 3: 8
Option 4: 10
Correct Answer: 8
Solution :
Given: A metallic sphere each has a diameter of 6 cm and a solid cylinder has an 8 cm diameter and height of 18 cm.
The volume of a sphere = $\frac{4}{3}\pi R^3$ and the volume of a cylinder = $\pi r^2h$, where $R$ is the radius of the sphere and $r,h$ are the radius and height of the cylinder.
Let the required number of spheres be $n$.
According to the question,
$n×\frac{4}{3}\pi R^3=\pi r^2h$
⇒ $4×n×(\frac{6}{2})^3=3×(\frac{8}{2})^2×18$
⇒ $n=\frac{3×16×18}{4×27}=8$
Hence, the correct answer is 8.
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