Question

PRE PER
The volume of two spheres are in the ratio 27:8. find their ratio of surface area?
SECTI​

Answer 1

Answer :

➥ The surface area of ratio = 9:5

Given :

➤ Volume ratio = 27:8

To Find :

➤ Surface area ratio = ?

Solution :

$\bf{: \implies Volume = \dfrac{4}{3}\pi {r}^{3} }$

Let radius be "r₁" and "r₂"

$\tt{: \implies \dfrac{ \cancel{\dfrac{4}{3} \pi } {r_{1}}^{3} }{ \cancel{\dfrac{4}{3} \pi}{r_{2}}^{3}} = \dfrac{27}{8} }$

$\tt{:\implies \dfrac{ r_{1}}{ r_{2}} = \sqrt[3]{\dfrac{27}{8}}}$

$\tt{:\implies \dfrac{ r_{1}}{ r_{2}} = \dfrac{3}{2} }$

Surface area = 4πr²

$\tt{: \implies \dfrac{ \cancel{4\pi} r_{1}^{2} } { \cancel{4\pi} r_{2}^{3}}}$

$\tt{: \implies \dfrac{r_{1}^{2}}{r_{2}^{2}} }$

$\tt{: \implies \dfrac{ {(3)}^{2} }{ {(2)}^{2} } }$

$\tt{: \implies \dfrac{9}{4} }$

$\tt{: \implies \green{ \underline{ \overline{ \boxed{ \purple{ \bf{ \: \: 9:4 \: \: }}}}}}}$

Hence, the surface area ratio is 9:4.