ABC26GN5078 · Volume and Surface Area

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

A solid piece of iron is in the form of a cuboids of dimensions (49cm × 33cm × 24cm) is melted and moulded to form a solid sphere. The radius of the sphere is [DMRC-Train Operator (Station Controller) Exam, 2016]

(a)19cm

(b)21cm

(c)23 cm

(d)25cm

Answer

Answer (as printed): B

Explanation

Let radius of sphere be $r \mathrm{cm}$. ∴ Volume of sphere = volume of cuboid $\Rightarrow \frac{4}{3} \pi r^{2}=L \times b \times h$ $\Rightarrow \frac{4}{3} \pi r^{3}=49 \times 33 \times 24$ $\Rightarrow \frac{4}{3} \times \frac{22}{7} \times r^{3}=49 \times 33 \times 24$ $\Rightarrow r^{3}=\frac{49 \times 33 \times 24 \times 3 \times 7}{4 \times 22}$ $\Rightarrow r^{3}=9261$ $\therefore r=\sqrt[3]{9261}=\sqrt[3]{21 \times 21 \times 21}=21 \mathrm{cm}$.

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