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Question

The largest sphere is carved out of a cube of edge 14 cm. The volume of this sphere is:


A
1370 cm3
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B
1800 cm3
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C
1437 cm3
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D
1734 cm3
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Solution

The correct option is D 1437 $$\text{cm}^3$$
The largest sphere that can be carved out of a cube will have diameter equal to length of the side of the cube.
Diameter $$ = 14\, \text{cm}$$
$$ \Rightarrow$$ Radius, $$r = 7\ \text{cm} $$
Volume of the sphere, $$V=\dfrac{4}{3} \pi r^3$$
$$ \therefore V = \dfrac{4}{3}\pi r^{3} $$
         $$= \dfrac{4}{3}\times \dfrac{22}{7}\times 7\times 7 \times 7\ \text{cm}^3$$ 
         
         $$ = \dfrac{88}{3}\times 49\, \text{cm}^{3} $$
         $$ = 1437.33\, \text{cm}^{3} $$ 


Mathematics

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