ABC26GN5006 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2009 · Marks: · Difficulty:
If three metallic spheres of radii 6 cms, 8 cms and 10 cms are melted to form a single sphere, the diameter of the new sphere will be
(a)12 cms
(b)24 cms
(c)30 cms
(d)36 cms
Answer
Explanation
Volume of new sphere $$\begin{aligned} & =\left[\frac{4}{3} \pi \times(6)^{3}+\frac{4}{3} \pi \times(8)^{3}+\frac{4}{3} \pi \times(10)^{3}\right] \mathrm{cm}^{3} \\ & =\left\{\frac{4}{3} \pi\left[(6)^{3}+(8)^{3}+(10)^{3}\right]\right\} \mathrm{cm}^{3} \\ & =\left(\frac{4}{3} \pi \times 1728\right) \mathrm{cm}^{3}=\left[\frac{4}{3} \pi \times(12)^{3}\right] \mathrm{cm}^{3} . \end{aligned}$$ Let the radius of the new sphere be $R$. Then, $\frac{4}{3} \pi R^{3}=\frac{4}{3} \pi \times(12)^{3} \Rightarrow R=12 \mathrm{cm}$. ∴ Diameter $=2 R=24 \mathrm{cm}$.
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