Explanation
Consider the given surface area of sphere $$=324\pi \,c{{m}^{3}}$$
Let, radius of sphere =r
We know that,
Surface area of the sphere$$=4\pi {{r}^{2}}\,c{{m}^{3}}$$
Now,
$$ 4\pi {{r}^{2}}=324\pi $$
$$ {{r}^{2}}=81 $$
$$ r=9\,cm $$
$$ \dfrac{4}{3}\pi {{r}^{3}}=4851 $$
$$ {{r}^{3}}=\dfrac{3\times 4851\times 7}{4\times 22} $$
Now, volume of the sphere,
$$ =\dfrac{4}{3}\pi {{r}^{3}} $$
$$ =\dfrac{4}{3}\pi \times {{9}^{3}}c{{m}^{3}} $$
$$ =972\pi c{{m}^{3}} $$
Hence, this is the answer.
Given, the diameter of the sphere $$=2p\,cm$$
radius = $$2p/2$$ = $$p$$
We know that the volume of the sphere
$$ =\dfrac{4}{3}\pi {{\left( 2p \right)}^{3}} $$
$$ =\dfrac{4}{3}\pi {8{p}^{3}}\,c{{m}^{3}} $$
$$ =\dfrac{32}{3}\pi {{p}^{3}}\,c{{m}^{3}} $$
Given, the radius of the sphere $$=r\,cm$$.
If the sphere is divided into two equal parts, then the resulting parts are hemispheres with radius $$=r\,cm$$.
Therefore, the total surface area of each hemisphere $$=3\pi {{r}^{2}}$$
Then, the total surface area of both hemisphere $$=2\times 3\pi {{r}^{2}}=6\pi {{r}^{2}}\,c{{m}^{2}}$$.
Hence, option $$D$$ is correct.
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