Surface Areas and Volumes Test - 32

Given, the diameter of the sphere $$=2p\,cm$$

 radius = $$2p/2$$ = $$p$$

We know that the volume of the sphere

$$ =\dfrac{4}{3}\pi {{r}^{3}} $$

$$ =\dfrac{4}{3}\pi {{\left( 2p \right)}^{3}} $$

$$ =\dfrac{4}{3}\pi {8{p}^{3}}\,c{{m}^{3}} $$

$$ =\dfrac{32}{3}\pi {{p}^{3}}\,c{{m}^{3}} $$

Hence, this is the answer.

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.

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.