Question

how many spherical bullets can be made out of a solid cube of lead whose edge measure 44 cm, each Bullet being 4 cm in diameter​

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\small{\underline{\red{\rm{Given:}}}}$

• $\rm{SIDE\:_{cube}=44cm}$

• $\rm{DIAMETER\:_{bullet}=4cm}$

• $\rm{RADIUS\:_{bullet}=2cm}$

$\small{\underline{\green{\rm{To\:Find:}}}}$

• $\rm{NUMBER\:_{bullet}}$

$\small{\underline{\red{\rm{At\:1st\: calculate\: their\: Volume:}}}}$

$\rm\orange{\longrightarrow Volume\:_{bullet}=\dfrac{4}{3}\pi\:r^3}$

$\rm{\implies Volume\:_{bullet}=\dfrac{4}{3}*\dfrac{22}{7}*2^3}$

$\rm{\implies Volume\:_{bullet}=\dfrac{4*22*8}{3*7}}$

$\rm\orange{\longrightarrow Volume\:_{cube}=S^3}$

$\rm{\implies Volume\:_{cube}=44^3}$

$\rm{\implies Volume\:_{cube}=44*44*44}$

Hence,

$\rm\orange{\longrightarrow NUMBER\:_{bullet}=\dfrac{Volume\:of\:solid\:cube}{Volume\:of\: bullet}}$

$\rm{\implies NUMBER\:_{bullet}=\dfrac{44*44*44*3*7}{4*22*8}}$

$\rm\purple{\implies NUMBER\:_{bullet}=2541\: bullet's}$

$\sf{Some\: related\: formula}$

• $\rm{C.S.A\:of\: Sphere=4\pi\:r^2}$

• $\rm{C.S.A\:of\:Cube=4(s^2)}$

• $\rm{T.S.A\:of\:Cube=6(s^2)}$

Answer 2

$\large\red{\underline{\underline{\bf{\blue{Given}}}}}$

• Side of cube = 44 cm

• Diameter of Spherical bullets = 4cm

$\large\red{\underline{\underline{\bf{\blue{To Find}}}}}$

• Number of Spherical bullets

$\large\red{\underline{\underline{\bf{\blue{Solution}}}}}$

First we have to find,

➠ Volume of Cube = a³

➠ Volume of Cube = 44³ = 85184 cm³

Now,

We have to find,

➠ Volume of Sphere = 4/3πr³

➠ Diameter (d) = 4cm. --(given)

So,

➠ Radius (r) = d/2 = 4/2 = 2cm

Now,

$Volume \: = \frac{4}{3} \times \frac{22}{7} \times {2}^{3} \\ \\ \implies \: \frac{32 \times 22}{7 \times 3} \\ \\ \implies \: \frac{704}{21} {cm}^{3}$

Now,

➪ Number of Spherical bullets =

$\frac{Volume \: of \: Cube}{Volume \: of \: Sphere}$

Hence,

➪ Number of Bullets =

$\implies \: \frac{85184}{ \frac{704}{21} } \\ \\ \implies \: 85184 \times \frac{21}{704} = 121 \times 21 = 2541$

Hence,

➥ Number of Bullets = 2541

➲ More Formulas :-

Cube ➘

• Volume of Cube = a³

• Total Surface Area = 6a²

• Length of Diagonal = √3a

Sphere ➘

• Volume of Sphere = 4/3πr³

• Total Surface Area = 4πr²