RRB Technician 2014 Ques 7
Question: The radius of the internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. If it is melted and recast into a solid cylinder of height $ 2\frac{2}{3}cm. $ . What is the diameter of the cylinder?
Options:
A) 12 cm
B) 7 cm
C) 14 cm
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- Internal volume of shell $ =\frac{4}{3}\pi {{(3)}^{3}}cm^{3} $ External volume of shell $ =\frac{4}{3}\pi {{(5)}^{3}}cm^{3} $
$ \therefore $ Volume of metal $ =\frac{4}{3}\pi {{(5)}^{3}}-\frac{4}{3}\pi {{(3)}^{3}} $ $ =\frac{4}{3}\pi (125-27) $ $ =\frac{4}{3}\pi \times 98 $ Length of cylinder $ =\frac{8}{3},cm $
$ \therefore $ Volume of cylinder formed $ =\frac{4}{3}\pi \times 98 $
$ \Rightarrow $ $ \pi r^{2}h=\frac{4}{3}\pi \times 98 $
$ \Rightarrow $ $ r^{2}=\frac{4}{3}\times 98\times \frac{3}{8} $
$ \Rightarrow $ $ r^{2}=49 $
$ \therefore $ $ r=7cm $ Here, diameter of cylinder $ =2\times 7=14cm $
BETA
