Question

how many lead shots each of radius 6cm can be made out of a rectangular slab of dimensions 44cm.24.cm.36m​

Answer 1

AnsWer :

42.

Correct QuestioN :

how many sphercal lead shots each of radius 6 cm can be made out of a rectangular slab of dimensions 44cm 24 cm 36cm.

SolutioN :

We know,

• Volume of Sphere = 4 / 3 πr³.
• Rectangular slab = 44 , 24 , 36.

Let,

• Radius ( R )
• Rectangular slab = L * B * H
• No of lead shots formed be N.

$\tt \dagger \: \: \: \: \: Number \: of \: lead \: shots \: formed = \dfrac{ Volume \: of \: lead \: Rectangular \: slab }{ Volume \: of \: One \: sphere}$

$\tt \longmapsto N= \dfrac{ 44 \times 24 \times 36 }{ \dfrac{4}{3} \pi {r}^{3} }$

• Note : π = 22 / 7.
• R = 6 cm.

$\tt \longmapsto N = \dfrac{ 44 \times 24 \times 36 }{ \dfrac{4}{3} \times \dfrac{22}{7} \times 6 \times 6\times6 }$

$\tt \longmapsto N = \dfrac{ 44 \times 24 \times \cancel{36 }}{ \dfrac{4}{3} \times \dfrac{22}{7} \times \cancel 6 \times \cancel6 \times 6 }$

$\tt \longmapsto N = \dfrac{ 44 \times 24 \times 3 \times 7}{ {4} \times 6 \times {22}}$

$\tt \longmapsto N = \dfrac{ \cancel{44 }\times 24 \times 3 \times 7}{ {4} \times 6 \times { \cancel{22}}}$

$\tt \longmapsto N = \dfrac{ \cancel2 \times 24 \times 3 \times 7}{ \cancel{4} \times 6 }$

$\tt \longmapsto N = \dfrac{ \cancel{24} \times 3 \times 7}{ 6 \times \cancel2 }$

$\tt \longmapsto N = 2 \times 3 \times 7.$

$\tt \longmapsto N = 42.$

✡ Therefore, 42 lead shots can be made slab.

Answer 2

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{0.60 cm}\begin{picture}(12,4)\linethickness{0.27mm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\qbezier(6,6)(4,7.3)(4,7.3)\qbezier(6,9)(4,10.2)(4,10.3)\qbezier(11,9)(9.5,10)(9,10.3)\qbezier(11,6)(10,6.6)(9,7.3)\put(8,5.5){\sf{44 cm}}\put(3.5,6.3){\sf{24 cm}}\put(11.2,7.5){\sf{36 cm}}\thicklines\put(14.5,7.5){\circle{40}}\put(14.5,7.5){\circle*{.1}}\put(14.5,7.5){\line(1,0){1.2}}\put(14.5,7){\scriptsize\sf 6 cm}\end{picture}$

⠀⠀⠀$\rule{160}{1}$

⠀✩ Rectangular Slab of Cuboid Shape with ⠀⠀ dimensions 44 cm , 24 cm and 36 cm.

⠀✩ Lead Shot (Sphere) of radius 6 cm.

⠀

☢ $\underline{\boldsymbol{According\: to \:the\: Question :}}$

$:\implies\sf Vol.\:of\:Slab=Vol.\:of\:Shot \times Number\\\\\\:\implies\sf Vol.\:of\: Cuboid=Vol.\:of\: Sphere \times Number\\\\\\:\implies\sf L \times B \times H = \dfrac{4}{3}\pi r^3 \times Number\\\\\\:\implies\sf 44 \times 24 \times 36 = \dfrac{4}{3} \times \dfrac{22}{7} \times(6)^3 \times Number\\\\\\:\implies\sf \dfrac{44 \times 24 \times 36 \times 3 \times 7}{4 \times 22 \times 36 \times 6} = Number\\\\\\:\implies\sf Number =2 \times 3 \times 7\\\\\\:\implies\underline{\boxed{\sf Number = 42}}$

⠀

$\therefore\:\underline{\textsf{\textbf{42} lead shots can be made of slab}}.$