Question

The radius of sphere (in cm) whose volume is 12 π cm3 ?
a) 3
b) 3√3
c)3 2/3
d) 3 1/3​

Answer 1

$\sf \large \underbrace{ \underline{Understanding \: the \: Question}}$

As volume of sphere is given to be 12πcm³ so we can easily find the radius of the given sphere by applying formula of volume of sphere.

$\boxed{ \sf &#10029 Volume \: of \: sphere= \dfrac{4}{3} \pi \: {r }^{3} }$

$\sf \to \: 12\pi \: cm {}^{3} = \dfrac{4}{3} \pi \: {r}^{3}$

$\sf \to \: 12\pi \times \dfrac{3}{4 \times \pi} \: cm {}^{3} = {r}^{3}$

$\sf \to \: \cancel{12\pi \times \dfrac{3}{4 \times \pi} \:} cm {}^{3} = {r}^{3}$

$\sf \to 9 {cm}^{3} = {r}^{3}$

$\sf \to\sqrt{3} \times \sqrt{3} \times \sqrt{3} \times \sqrt{3} = {r}^{3}$

$\sf \to 3 \sqrt{3} = r$

Hence the radius of sphere is 3√3cm.

So option (B) is correct.

$\sf \Large \underbrace{ \underline{Additional \: information}}$

More formulae:

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

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