Question

Find the number of spherical lead shots each of diameter 6 cm that can be made from a solid cuboid of lead having dimensions 24cmx22cmx12cm

Answer 1

$Diameter\: of \: each \: Spherical \:lead \\shot (d) = 6 \:cm$

$Radius \: the \:shot (r) = \frac{d}{2} \\= \frac{6}{2} \\= 3 \:cm$

$\underline {\blue { Dimensions \:of \: a \:solid\:cubiod : }}$

$Length (l) = 24 \:cm, \\ Breadth (b) = 22\:cm \\and \: Height (h) = 12 \:cm$

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

$\boxed {\pink { n = \frac{Volume _{cuboid }}{Volume_{lead \:shot }} }}$

$\implies n = \frac{l \times b \times h }{\frac{4}{3} \pi r^{3}} \\= \frac{ 24 \times 22 \times 12 }{ \frac{4}{3} \times \frac{22}{7} \times 3^{3}}$

$= \frac{ 24 \times 22 \times 12\times 3 \times 7}{4 \times 22 \times 27 }$

$= 56$

Therefore.,

$\red{number \:of \: Spherical \:lead \: shots }\\\red{made} \green {= 56}$

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Answer 2

Given dimensions,

l = 24 cm b = 22 cm,h = 12 cm

diameter = 6 cm

its radius = 6/2

= 3 cm

Now,

Volume of cuboid

No. of lead shots = _______________

Volume of sphere

(l × b × h)

= _________

4/3πr^3

(24 × 22 x 12 x 3)

= _______________

(π × 3 × 3 × 3 × 4)

= 56

Explanation:

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