Question

How manyy spherical balls can be made out & solid cylinder for lead whose
radius and height is 14 cm& each ball being 3.5cm in diameter​

Answer 1

Correct Question :

How many spherical balls can be made out of solid cylinder of lead whose radius and height is 14 cm and each ball being 3.5 cm in diameter.

AnswEr :

Volume of Cylinder and Spherical Balls will be Same, with Given Parameters.

$:\implies\scriptsize{\texttt{Volume of Cylinder = Volume of Spherical Balls \times Number of Balls}}\\\\\\:\implies\tt \pi r^2h = \dfrac{4}{3}\pi R^3 \times Number\\\\\\:\implies\tt {r}^{2}h = \dfrac{4}{3}{R}^{3} \times Number\\\\\\:\implies\tt{(14)}^{2} \times 14 =\dfrac{4}{3} \times { \bigg(\dfrac{3.5}{2} \bigg)}^{3} \times Number\\\\\\:\implies\tt14 \times 14 \times 14 = \dfrac{4}{3} \times \dfrac{35 \times 35 \times 35}{8 \times 1000}\times Number\\\\\\:\implies\tt \dfrac{14 \times 14 \times14 \times 3 \times 8000}{4 \times 35 \times 35 \times 35} = Number\\\\\\:\implies\tt \dfrac{2 \times 2 \times 2 \times 3 \times 2000}{5 \times 5 \times 5} = Number\\\\\\:\implies\tt 24 \times 16 = Number\\\\\\:\implies\boxed{\red{\tt Number = 384}}$

⠀

$\therefore\:\underline{\textsf{Number of Spherical Balls can be made is \textbf{384.}}}$

Answer 2

Answer:

spherical balls = 384

Step-by-step explanation:

V of CYLINDER = πr^2h

V of SPHERE = 4/3πr^3

v of cylinder = π×14×14×14

v of sphere = 4/3×π×3.5/2×3.5/2×3.5/2

= 1/3×π×3.5×3.5×3.5/2

NO OF SPHERICAL BALLS =

V of cylinder / v of sphere

= π×14×14×14 / 1/3×π×3.5×3.5×3.5/2

= 14×14×14×3×2 / 3.5×3.5×3.5

= 4×4×4×3×2

= 16×24

=384

HOPE IT WILL HELP U.

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