Question : A solid sphere made of wax of radius 12 cm is melted and cast into solid hemispheres of radius 4 cm each. Find the number of such solid hemispheres.
Option 1: 54
Option 2: 27
Option 3: 14
Option 4: 28
Correct Answer: 54
Solution :
Given,
A solid sphere made of wax of radius 12 cm is melted and cast into solid hemispheres of radius 4 cm each.
Let the number of hemispheres thus formed be $n$.
⇒ Volume of sphere = $n$(Volume of hemisphere)
Volume of sphere = $\frac43\pi r^3$, where r is the radius of the sphere
And, Volume of hemisphere = $\frac23\pi R^3$, where R is the radius of the hemisphere
⇒ $\frac43\pi r^3=n(\frac23\pi R^3)$
⇒ $2r^3=nR^3$
⇒ $2(12)^3=n\times(4)^3$
⇒ $n=\frac{2\times12\times12\times12}{4\times4\times4}$
⇒ $n=2\times3\times3\times3$
⇒ $n=54$
Hence, the correct answer is 54.
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