Question

If the area of curved surface and tje volume of a sphere are x² unit and y³ unit respectively then find the value of x³ / y³​

Answer 1

Given :

• Area of curved surface of sphere =x² units

• The volume of sphere =y³ units

To find :

$\red\bigstar\boxed{\sf{The \: value \: of \: \dfrac{x^{3}}{y^{3}}=?}}$

Formula :

$\red \bigstar \boxed{ \sf{area \: of \: curved \: surface \: of \: sphere = 4\pi {r}^{2} }}$

$\\ \red \bigstar \boxed{ \sf{volume \: of \: sphere \frac{4}{3} \pi {r}^{3} }}$

Solution :

$\\ \implies \sf\frac{ {x}^{3} }{ {y}^{3} } = \frac{area \: of \: curved \: surface \: of \: sphere}{volume \: of \: sphere}$

$\\ \implies \sf \: \frac{ {x}^{3} }{ {y}^{3} } = \frac{4\pi {r}^{2} }{ \frac{4}{3}\pi {r}^{3} } \\ \\ \\ \implies \sf \: \frac{ {x}^{3} }{ {y}^{3} } = \frac{ \cancel {4\pi {r}^{2} } }{ \cancel {\frac{4}{3} \pi {r}^{3} } } \\ \\ \\ \implies \sf \: \frac{ {x}^{3} }{ {y}^{3} } = \frac{1}{ \frac{1}{3} r} \\ \\ \\ \implies \boxed{\sf{ \: {x}^{3} = 3r {y}^{3} \: \: \: and \: \: {y}^{3} = \frac{ {x}^{3} }{3r}}}$