Question

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

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

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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