Question

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. The radius of the sphere is

(a) 19 cm (b) 21 cm (c) 23 cm (d) 25 cm

Answer 1

Let the radius of the sphere be R cm.

Dimension of the cuboid $=49cm\times 33cm\times 24cm.$

Volume of cuboid $=49\times 33\times 24c{m}^3=38808c{m}^3$​​​​​​​

Volume of sphere $=\frac{4}{3}\pi R^3$​​​​​​​ ​​​​​​​​​​​​​​

Since, the solid piece of iron in the cuboidal form is moulded into a sphere,

∴ Volume of sphere = Volume of cuboid

$\frac{4}{3}\pi R^3=38808c{m}^3\frac{4}{3}\times \frac{22}{7}\times R^3=38808\frac{88}{21}\times R^3=38808R^3=\frac{38808}{\frac{88}{21}}{R}^3=\frac{38808\times 21}{88}{R}^3=9261R=\sqrt[3]{39261}=\sqrt[3]{321\times 21\times 21}R=21cm$

Thus, the radius of sphere is 21 cm.