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Volume and Surface Area — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsVolume and Surface Area3 Marks
Question
Find the volume of a sphere whose surface area is $154cm^2$. $\big(\text{Take}\ \pi=\frac{22}{7}\big).$
✓

Answer

Let the radius of the sphere be r cm. Surface area of the sphere $= 154cm^2$
$\therefore4\pi\text{r}^2=154$
$\Rightarrow4\times\frac{22}{7}\times\text{r}^2=154$
$\Rightarrow\text{r}=\sqrt{\frac{154\times7}{4\times22}}=\sqrt{1225}$
$\Rightarrow\text{r}=3.5\text{cm}$
$\therefore$ Volume of the sphere $=\frac{4}{3}\pi\text{r}^3=\frac{4}{3}\times\frac{22}{7}\times(3.5)^3\approx179.67\text{m}^3$
​​​​​​​Thus , the volume of the sphere is approximately $179.67m^3.$

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