Question

The number of solid of solid spheres, each of diameter 6cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is:

• A. 3
• B. 5
• C. 4
• D. 6

Answer 1

The correct option is B

5

Let r and h be the radius and the height of the cylinder, respectively.
Given : Diameter of the cylinder = 4cm
$\therefore$ Radius of the cylinder, r = 2cm
Height of the cylinder, h = 45cm
Volume of the solid cylinder $=\pi r^{2}h=\pi \times (2{)}^2\times 45c{m}^3=180\pi c{m}^3$
Suppose the radius of each sphere be R cm.
Diameter of the sphere = 6cm
$\therefore$ Radius of the sphere, R = 3cm
Let n be the number of solids formed by meltiong the solid metallic cylinder.
$\therefore$ n $\times$ Volume of the solid spheres = Volume of the solid cylinder
$\Rightarrow n\times \frac{4}{3}\pi R^3=180\pi$
$\Rightarrow n\times \frac{4}{3}\pi 3^3=180\pi$
$\Rightarrow n=\frac{180\times 3}{4\times 27}=5$
Thus, the number of solid spheres that can be formed is 5.
Hence, the correct option is B.