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Question

The largest sphere is carved out of a cube of side 10.5 cm. Find the volume of the sphere.


A
606.375cm3
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B
66.3cm3
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C
60.375cm3
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D
66.375cm3
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Solution

The correct option is A $$ 606.375\,cm^{3}$$
We have,
Diameter of the largest sphere$$ = 10.5 cm\Rightarrow 2r = 10.5 cm \Rightarrow  r = 5.25\, cm$$
$$ \therefore $$ Volume of the sphere$$ = \dfrac{4}{3} \times \dfrac{22}{7} \times \left ( 5.25 \right )^{3} \,cm^{3}$$
$$ = \dfrac{4}{3} \times \dfrac{22}{7} \times \left ( \dfrac{21}{4} \right )^{3} cm^{3} = 4 \times 22 \times \dfrac{21^2}{64} cm^3 $$
$$ = \dfrac{11 \times 441}{ 8 } \,cm^3 = 606.375\, cm^3 $$

Mathematics

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