Question

Question 12
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. the diameter of each sphere is
(A) 4 cm
(B) 3 cm
(C) 2 cm
(D) 6 cm

Answer 1

Option (C) is correct.
Given, diameter of the cylinder = 2 cm
$\therefore$ Radius = 1 cm and height of the cylinder = 16 cm $[Diameter=2\times radius]$
$\therefore$ Volume of the cylinder $=\pi \times (1{)}^{2}16=16\pi c{m}^3$ [Volume of cylinder $=\pi \times (radius{)}^2\times height$]
Now, let the radius of solid sphere = r cm
Then, its volume $=\frac{4}{3}\pi r^{3}c{m}^3$ [ Volume of sphere $=\frac{4}{3}\times \pi \times \left(radius{)}^3\right]$
According to the question,
Volume of the twelve solid sphere = Volume of cylinder
$12\times \frac{4}{3}\pi r^3=16\pi r^3=1\Rightarrow r=1cm\therefore diameterofeachsphere,d=2r=2\times 1=2cm$
Hence the required diameter of each sphere is 2 cm