Surface Area And Volume of Sphere — Maths STD 9 — Question
Gujarat BoardEnglish MediumSTD 9MathsSurface Area And Volume of Sphere3 Marks
Question
Find the volume of a sphere whose surface area is $154cm2.$
✓
Answer
In the given problem, we have to find the volume of a sphere whose surface area is given.
So, let us first find the radius of the given sphere.
Surface area of the sphere $(S)$ $= 154cm^2$
Let the radius of the sphere be $r\ cm$
Now, we know that surface area of the sphere
$=4\pi\text{r}^2$
So, $154=4\Big(\frac{22}{7}\Big)(\text{r})^2$
$\text{r}^2=\frac{(154)(7)}{(4)(22)}$
$\text{r}^2=12.25$
Further, solving for r $\text{r}=\sqrt{12.25}$
$\text{r}=3.5$
Therefore, the radius of the given sphere is $3.5\ cm$.
Now, the volume of the sphere $=\frac{4}{3}\pi\text{r}^3$
$=\Big(\frac{4}{3}\Big)\Big(\frac{22}{7}\Big)(3.5)^3$
$=179.66\text{cm}^3$
Therefore, the volume of the given sphere is $179.66\ cm^3.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.