A Silver cup has a shape of a hemisphere surmounted by cylinder. The common diameter is 10.5 cm The total height is 11.25 cm. find its volume?

Consider the figure,

Here, we need to find the volume of a silver cup. So, we are given
Diameter of the hemisphere = 10.5 cm
Radius of the hemisphere (r) = $\left(\frac{10.5}{2}\right)cm$
  = 5.25 cm
Volume of the hemisphere (V) = $\frac{2}{3}{\mathrm{\pi r}}^3$
          $$\begin{gathered} =\left(\frac{2}{3}\right)\left(\frac{22}{7}\right){\left(5.25\right)}^3 \\ =\left(\frac{44}{21}\right)\left(144.70\right) \\ =\frac{6366.94}{21} \\ =303.19c{m}^3 \end{gathered}$$

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Also, for the cylinder
Radius (r) = 5.25 cm
Height (h) = (11.25-5.25) cm
  = 6 cm
Volume (V₁) = ${\mathrm{\pi r}}^2\mathrm{h}$
        $$\begin{gathered} =\left(\frac{22}{7}\right){\left(5.25\right)}^2\left(6\right) \\ =\frac{3638.25}{7} \\ =519.75{\mathrm{cm}}^3 \end{gathered}$$

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So,
Volume of silver cup = V + V₁
  = (303.19 + 519.75) cm³
  = 822.94 cm³
Therefore, the volume of the silver cup is 822.94 cm³