Surface Areas and Volumes — Maths STD 9 — Question

2. 4851cm³

Solution:

Surface area of sphere $=4\pi\text{r}^2$

Given surface area = 1386cm²

$\Rightarrow4\times\frac{22}{7}\times\text{r}^2=1386$

$\Rightarrow\text{r}^2=\frac{1386\times7}{88}=\frac{441}{4}$

$\Rightarrow\text{r}=\frac{21}{2}$

Volume of sphere $=\frac{4}{3}\pi\text{r}^3$

Volume $=\frac{4}{3}\pi\Big(\frac{21}{2}\Big)^3$

$=\frac{4}{3}\times\frac{22}{7}\times\Big(\frac{21}{2}\Big)^3$

$=4851\text{cm}^2$