A solid piece of metal in the form of a cuboid of dimensions $\displaystyle 11$ cm × $\displaystyle 7$ cm × $\displaystyle 7$ cm is melted to form 'n' number of solid spheres of radii $\displaystyle \frac{7}{2} \mathrm{~cm}$ each. Find the value of n.

\[\begin{array}{l} n \times \frac{4}{3} \times \frac{22}{7} \times\left(\frac{1}{2}\right)=11 \times(7)^{2} \\ \Rightarrow n=3 \end{array} \]In Fig. $\displaystyle 1$, AB is diameter of a circle centered at $\displaystyle \mathrm{O} . \mathrm{BC}$ is tangent to the circle at B . If OP bisects the chord AD and $\displaystyle \angle \mathrm{AOP}=60^{\circ}$, then find $\displaystyle \mathrm{m} \angle \mathrm{C}$.Fig. $\displaystyle 1$ \[\begin{array}{c} \because A P=P D \Rightarrow O P \perp A D \\ \therefore \angle O A P=30^{\circ} \end{array} \]Also $\displaystyle \angle A B C=90^{\circ}$ \[\Rightarrow \angle C=60^{\circ} \]OrIn Fig. $\displaystyle 2$, XAY is a tangent to the circle centered at O . If $\displaystyle \angle \mathrm{ABO}=40^{\circ}$, then find $\displaystyle \mathrm{m} \angle \mathrm{BAY}$ and $\displaystyle \mathrm{m} \angle \mathrm{AOB}$.Fig. $\displaystyle 2$ \[\begin{array}{l} O A=O B \Rightarrow \angle O A B=40^{\circ} \\ O A \perp A Y \Rightarrow \angle B A Y=50^{\circ} \\ \angle A O B=180^{\circ}-80^{\circ}=100^{\circ} \end{array} \]