Explanation
Given, radius $$r=2.8$$ cm.
We know that, the surface area of a sphere of radius $$r$$ $$= 4\pi { r }^{ 2 } $$
$$= 4 \times \dfrac {22}{7} \times 2.8 \times 2.8 $$
$$= 98.56 {cm}^{2} $$.
Let radius of sphere be $$r$$ cm.
We know, surface area of sphere $$=4\pi { r }^{ 2 }$$
$$\implies$$ $$221.76 cm^2 =4\pi { r }^{ 2 }$$
$$\implies$$ $$ { { r }^{ 2 } }=\cfrac { 221.76 }{ 4\pi } =\dfrac{221.76\times 7}{4\times 22}=17.64$$
$$\implies$$ $$ r=\sqrt { 17.64 } =4.2 cm$$ .
Then, diameter of the sphere, $$d=2r=2\times4.2=8.4 cm$$.
Therefore, option $$A$$ is correct.
The formula for calculating the surface area of a cuboid of dimensions :
$$ l \times b \times h $$ is :
$$ 2\times (l\times b+b\times h+h\times l) $$
Substituting,
$$l=10cm$$
$$b=4cm$$
$$h=3cm$$
Surface area = $$ 2\times (10\times 4+4\times 3+3\times 10) $$
$$ = 2\times (40 + 12 + 30) $$
$$ = 2\times 82 { cm }^{ 2 } $$
$$ = 164 { cm }^{ 2 } $$
Hence, the answer is option (C)
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