Question

what is the total number of solid sphere each diameter 9 cm. which could be moulded to form a solid metal cylinder of a length 94.5 and diameter 6 cm?


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Answer 1

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The volume of sphere is equal to
$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge \frac{4}{3}\pi {r}^{3}$
Given :

The diameter =9
Radius=d/2=9/2=4.5

$\frac{4}{ \cancel{3 \: \: }} \times \frac{22}{7} \times \cancel{ 4.5}^{1.5} \times 4.5 \times 4.5 = 381.81cm^{3}$
Then, As we know the the volume of cylinder
$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge \rightarrow \huge\pi {r}^{2} h$
Given:
Length=94.5,R=d/2=6/2=3

$\frac{22}{ \cancel{7 \: \: }} \times {3}^{2} \times \cancel{94.5}^{13.5} = 2673 {cm}^{3}$
Then,

$\tiny Total \: no. \: spheres = \frac{the \:volume \: of \: solid \: cylinder}{the \: volume \: of \:each \: shpere}$
$\huge= \frac{2673}{381.81} = 7 \: \small{sphere's} \\ \\\tiny\rightarrow \: so, \: \: that \: the \: solid \: cylinder \: can \: contains \: 7 \: spheres \: only.$
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