Question

Fifteen identical spheres are made by melting a solid cylinder of radius 10 cm and height 5.4 cm, the diameter of each sphere is _________.

Answer 1

Let the radius of each sphere be r.

Radius of the cylinder, R = 10 cm

Height of the cylinder, H = 5.4 cm

It is given that, 15 identical spheres are made by melting a solid cylinder of radius 10 cm and height 5.4 cm.

∴ 15 × Volume of each sphere = Volume of the cylinder

$\Rightarrow 15\times \frac{4}{3}\mathrm{\pi }{r}^3=\mathrm{\pi }{R}^{2}H$

$\Rightarrow r^3=\frac{{\left(10\mathrm{cm}\right)}^2\times 5.4\mathrm{cm}}{20}$

$\Rightarrow r^3=27{\mathrm{cm}}^3$

$\Rightarrow r^3={\left(3\mathrm{cm}\right)}^3$

$\Rightarrow r=3\mathrm{cm}$

∴ Diameter of each sphere = 2r = 2 × 3 cm = 6 cm

Thus, the diameter of each sphere is 6 cm.

Fifteen identical spheres are made by melting a solid cylinder of radius 10 cm and height 5.4 cm, the diameter of each sphere is ___6 cm___.