Question

The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is [CBSE 2014]
(a) 3
(b) 5
(c) 4
(d) 6

Answer 1

Let the number of solid spheres be n.
Now, Volume of n solid sphere = Volume of cylinder

$$\begin{gathered} \Rightarrow n\times \frac{4}{3}\times \frac{22}{7}\times {\left(\frac{6}{2}\right)}^3=\frac{22}{7}\times {\left(\frac{4}{2}\right)}^2\times 45 \\ \Rightarrow n\times \frac{4}{3}\times 27=4\times 45 \\ \Rightarrow n=5 \end{gathered}$$

Hence, the correct answer is option B.