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Question
A solid metallic sphere of radius 3 cm is melted and recast into the shape of a solid cylinder of radius 2 cm. Find the height of the cylinder.
Sum
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Solution
Given: Radius of sphere \[r_{1} = 3\ \mathrm{cm}\]
Radius of cylinder \[r_{2} = 2\ \mathrm{cm}\]
To find: Height of cylinder [h]
Formula: Volume of cylinder = Volume of sphere
\[\pi r_{2}^{2} h = \dfrac{4}{3}\pi r_{1}^{3}\]
Substitution: \[\pi \times 2^{2} \times h = \dfrac{4}{3} \times \pi \times 3^{3}\]
Calculation: \[4h = \dfrac{4}{3} \times 27\]
\[4h = 36\]
\[h = \dfrac{36}{4} = 9\ \mathrm{cm}\]
Answer: \[h = 9\ \mathrm{cm}\]
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