Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2016 · Marks: · Difficulty:
If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, then the diameter of the new sphere will be
(a)12 cm
(b)24 cm
(c)30 cm
(d)36 cm
Answer
Answer (as printed): B
Explanation
Given Raddi of three metallic spheres be $r_{1}, r_{2} r_{3}$ are 6cm, 8cm and 10cm respectively. Let the radius of the new sphere be $R$. $$\begin{aligned} & \frac{4}{3} \pi R^{3}=\frac{4}{3} \pi\left(r_{1}^{3}+r_{2}^{3}+r_{3}^{3}\right) \\ & \frac{4}{3} \pi R^{3}=\frac{4}{3} \pi\left(6^{3}+8^{3}+10^{3}\right) \\ & R^{3}=(216+512+1000)=1728 \\ & \Rightarrow R=\sqrt[3]{12 \times 12 \times 12} \\ & R=12 \end{aligned}$$ Diameter $=24 \mathrm{cm}$