ABC26GN5030 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is
(a)$\sqrt{3} \mathrm{cm}$
(b)2 cm
(c)3 cm
(d)4 cm
Answer
Explanation
Let the radius of each sphere be $r \mathrm{cm}$. Then, Volume of 12 spheres = Volume of cylinder $$\begin{aligned} \Rightarrow 12 \times \frac{4}{3} \pi \times r^{3}=\pi \times 8 \times 8 \times 2 \Rightarrow & r^{3}=\left(\frac{8 \times 8 \times 2 \times 3}{12 \times 4}\right) \\ & \Rightarrow r=2 \mathrm{cm} . \end{aligned}$$ ∴ Diameter of each sphere $=2 r=4 \mathrm{cm}$.
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