Question

many solid cylinders of radius 3 cm and height 7 cm can be made
melting a solid sphere of radius 21 cm?
Activity : Radius of the sphere (r) = 21 cm
For cylinder, radius (r,) = 3 cm, height (11) = 7 cm
Number of cylinders that can be made =
Volume of the sphere
- we have not taken for
O
e(TT) i, ci
x 21 x 21 x 21​

Answer 1

$Given \: radius \:of \: a\: solid \: sphere (R) = 21\:cm$

$\underline { \blue { Dimensions \: of \: each \: cylinder :}}$

$radius (r) = 3 \:cm \:and \: height (h) = 7 \:cm$

/* According to the problem given */

If the solid sphere melted and cast into a solid cylinders of given measures . */

$Let \: the \: number \:of \: cylinders \: made =n$

$n = \frac{ Volume_{(sphere)}}{Volume_{(cylinder)}} \\= \frac{\frac{4}{3} \pi R^{3}}{\pi r^{2} h } \\= \frac{4 R^{3} }{ 3 \times r^{2} h } \\= \frac{ 4 \times 21^{3}}{ 3 \times 3^{2} \times 7 } \\= 196$

Therefore.,

$\red { Number \:of \: cylinders \: made \:by }\\\red { melting \:the \:sphere }\green {= 196}$

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