If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cylinder of base diameter 8 cm, then the height of the cylinder is :
Options:
A . 4 cm
B . $$\frac{13}{3}$$ cm
C . $$\frac{14}{3}$$ cm
D . 5 cm
Answer: Option C Let the height of the cylinder be h cm Then, $$\eqalign{ & \frac{4}{3}\pi \left[ {{{\left( 4 \right)}^3} - {{\left( 2 \right)}^3}} \right] = \pi \times {4^2} \times h \cr & \Rightarrow \frac{4}{3} \times \pi \times 56 = \pi \times 16h \cr & \Rightarrow h = \frac{{4 \times 56}}{{3 \times 16}} \cr & \Rightarrow h = \frac{{14}}{3}\,cm \cr} $$
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