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 rcm 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 3.5cm. Now, the volume of the sphere $=\frac{4}{3}\pi\text{r}^3$$=\Big(\frac{4}{3}\Big)\Big(\frac{22}{7}\Big)(3.5)^3$
$=179.66\text{cm}^3$
Therefore, the volume of the given sphere is $179.66cm^3.$
we have to find the volume of a sphere whose surface area is given.
So, let us first find the radius of the given sphere.
Surface area of the sphere (S) = $154cm^2$
Let the radius of the sphere be rcm Now,
we know that surface area of the sphere $=4\pi\text{r}^2$ So,$154=4\Big(\frac{22}{7}\Big)(\text{r})^2$
$\text{r}^2=\frac{(154)(7)}{(4)(22)}$
$\text{r}^2=12.25$
Further, solving for r$\text{r}=\sqrt{12.25}$
$\text{r}=3.5$
Therefore, the radius of the given sphere is 3.5cm. Now, the volume of the sphere $=\frac{4}{3}\pi\text{r}^3$$=\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 $179.66cm^3.$
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