Question

A metalic cylinder of diameter 5cm and height 10/3cm is melted and cast into a sphere what is diameter

Answer 1

Diameter of sphere is
$2 \sqrt[3]{25 \div 3}$
cm

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

$\textbf{\underline{D\;of\;Cylinder}}$

= 5 cm

${\boxed{\sf\:{R=\dfrac{D}{2}}}}$

$\tt{\rightarrow R=\dfrac{5}{2}}$

R = 2.5 cm

$\textbf{\underline{H\;of\;Cylinder}}$

$\tt{\rightarrow\dfrac{10}{3}}$

Now,

Using Formula :-

$\large{\boxed{Volume\;of\;Cylinder=\pi r^2h}}$

$\tt{\rightarrow\dfrac{22}{7}\times 2.5\times 2.5\times\dfrac{10}{3}}$

$\tt{\rightarrow\dfrac{1375}{21}}$

= 65.476 cu cm

$\textbf{\underline{Cylinder\;is\;melted\;cast\;into\;Sphere}}$

Hence,

$\textbf{\underline{Volume\;of\;Cylinder=Volume\;of\;Sphere}}$

Now,

${\boxed{\sf\:{Volume\;of\;Sphere=\dfrac{4}{3}\pi r^3}}}$

$\tt{\rightarrow 65.476=\dfrac{4}{3}\times\dfrac{22}{7}\times r^3}$

88r³ = 65.476 × 21

88r³ = 1374.996

= 1375

$\tt{\rightarrow r^3=\dfrac{1375}{89}}$

r³ = 15.625

r = 2.5

Therefore

$\textbf{\underline{Radius\;of\;sphere=2.5cm}}$

$\textbf{\underline{Diameter\;of\;Sphere}}$

= 2.5 × 2

= 5 cm