The volume of a hollow sphere is 11352/7cm^3.Its outer diameter is 16cm. Find its inner radius and its outer curved surface area.

Let R = external radius of the hollow sphere
Let r = internal radius of the hollow sphere
now, external diameter = 16 cm
so, external radius , R = 8 cm
volume of hollow sphere = $\frac{11352}{7} c{m}^3$

$$\begin{gathered} \Rightarrow \frac{4}{3}\mathrm{\pi }\left[{\mathrm{R}}^{3 }- r^3\right] = \frac{11352}{7} \\ \Rightarrow \frac{4}{3}\times \frac{22}{7}\left[8^3-r^3\right] = \frac{11352}{7} \\ \Rightarrow \left[512 -\mathit{ }{r}^3\right] = \frac{3\times 11352}{4\times 22} \\ \Rightarrow 512 -\mathit{ }{r}^3 = 387 \\ \Rightarrow r^3 = 512 - 387 = 125 \\ \Rightarrow r\mathit{ }= 5 \mathrm{cm} \\ \mathrm{so} \mathrm{internal} \mathrm{radius} = 5 \mathrm{cm} \\ \mathrm{Outer} \mathrm{CSA} \mathrm{of} \mathrm{hollow} \mathrm{sphere} = 4{\mathrm{\pi R}}^2 = 4\times \frac{22}{7}\times 8^2 =\frac{5632}{7} = 804.57 {\mathrm{cm}}^2 \end{gathered}$$