[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-
- A box of clay contains 25 packs
Each pack is a cuboid having dimensions 10cm × 10cm × 4 cm
To Find :-
- We have to find the no of spheres of radius 6cm can Jack make from a box of clay .
Let's Begin :-
Here, we have
- Length of one pack = 10cm
- Breath of 1 pack = 10 cm
- Height of 1 pack = 4 cm
We know that,
Volume of cuboid
[tex]\bold{\red{ = length }}{\bold{\red{\times{ breath }}}}{\bold{\red{\times{height}}}}[/tex]
Subsitute the required values,
[tex]\sf{ = 10 }{\sf{\times{ 10}}}{\sf{\times{4 }}}[/tex]
[tex]\sf{ = 100 }{\sf{\times{ 4}}}[/tex]
[tex]\bold{ = 400\: cm² }[/tex]
Thus, The volume of 1 pack is 400 cm²
Now,
We know that,
Volume of sphere
[tex]\bold{\pink{ = }}{\bold{\pink{\dfrac{4}{3}}}}{\bold{\pink{\pi{r^{3}}}}}[/tex]
Subsitute the required values,
[tex]\sf{ = }{\sf{\dfrac{4}{3}}}{\sf{\times{ 3.14 }}}{\sf{\times{(6)^{3}}}}[/tex]
[tex]\sf{ = }{\sf{\dfrac{4}{3}}}{\sf{\times{ 3.14 }}}{\sf{\times{216}}}[/tex]
[tex]\sf{ = 4}{\sf{\times{ 3.14 }}}{\sf{\times{72}}}[/tex]
[tex]\sf{ = 288}{\sf{\times{ 3.14 }}}[/tex]
[tex]\bold{ = 91.71 cm^{3}}[/tex]
Therefore,
No of spheres formed by 1 packs of cuboid
n = Volume of 1 packs/ Volume of sphere
Subsitute the required values,
[tex]\sf{ n = }{\sf{\dfrac{ 400}{91.71}}}[/tex]
[tex]\bold{ n = 4.36 }[/tex]
Thus, The number of spheres formed by 1 pack of cuboid are 4.36
Therefore,
Total number of spheres formed by 25 packs
[tex]\sf{ = 25 }{\sf{\times{ 4.36}}}[/tex]
[tex]\bold{ = 109 }[/tex]
Hence, The total number of spheres made by Jack from a box of clay is 109 spheres.
