Explanation
Let radius of sphere be $$r$$ cm.
Given, the surface area of a sphere $$=346.5\ \text{cm}^2$$.
We know, surface area of sphere $$=4\pi { r }^{ 2 }$$.
$$4\pi r^2 = 346.5 cm^2 $$
$$ { { r }^{ 2 } }=\cfrac { 346.5 }{ 4\pi } $$
$$=\dfrac{346.5\times7}{4\times22}$$
$$=\dfrac{2425.5}{4\times22}$$
$$=27.5625$$
$$\implies$$ $$ r=\sqrt { 27.5625 } =5.25\ \text{cm}$$ .
Therefore, option $$A$$ is correct.
False: Clearly from figure when a ball (spherical) is exactly fitted inside the cubical box then diameter of the ball becomes equal to side of cube so
Diameter $$= d = a$$
$$\Rightarrow$$ Radius $$=r=\dfrac{a}{2}$$
$$\therefore$$ Volume of spherical ball $$=\dfrac{4}{3}\pi r^{3}$$
$$=\dfrac{4}{3}\pi \left ( \dfrac{a}{2} \right )^{3}=\dfrac{4}{3}\pi \dfrac{a^{3}}{8}=\dfrac{1}{6}\pi a^{3}\neq \dfrac{4}{3}\pi a^{3}$$
Hence, the given statement is false.
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