Question

Question 10
A solid piece of iron in the form of a cuboid of dimensions $49cm\times 33cm\times 24cm$, is moulded to form a solid sphere. Then, radius of the sphere is
(A) 21 cm
(B) 23 cm
(C) 25 cm
(D) 19 cm

Answer 1

Option (A) is correct.
Given dimensions of the cuboid $=49cm\times 33cm\times 24cm$

Volume of cuboid $=length\times breadth\times height$
$\therefore$ Volume of the cuboid $=49\times 33\times 24=38808c{m}^3$
Let the radius of the sphere is r, then
Volume of the sphere = $\frac{4}{3}\pi r^3$
According to the question,
Volume of the sphere = Volume of the cuboid
$\frac{4}{3}\pi r^3=388084\times \frac{22}{7}{r}^3=38808\times 3r^3=\frac{38808\times 3\times 7}{4\times 22}=441\times 21r^3=21\times 21\times 21\therefore r=21cm$
Hence, the radius of the sphere is 21 cm.