ABC26GN5007 · Volume and Surface Area

Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:

A solid metallic sphere of radius 8 cm is melted and recast into spherical balls each of radius 2 cm. The number of spherical balls, thus obtained, is
(a)16
(b)48
(c)64
(d)82
Answer
Answer (as printed): C
Explanation
Volume of bigger sphere $$\begin{aligned} & =\left[\frac{4}{3}\pi\times(8)^3\right]\text{cm}^3=\left(\frac{4}{3}\pi\times512\right)\text{cm}^3. \\ & \text{Volume of 1 ball}=\left[\frac{4}{3}\pi\times(2)^3\right]\text{cm}^3=\left(\frac{4}{3}\pi\times8\right)\text{cm}^3. \\ & \therefore \text{Number of balls}=\left(\frac{\frac{4}{3}\pi\times512}{\frac{4}{3}\pi\times8}\right)=\frac{512}{8}=64. \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

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