Question : The largest sphere is carved out of a cube of side 7 cm. The volume of the sphere will be:
Option 1: 179.67 cm3
Option 2: 165.67 cm3
Option 3: 175.67 cm3
Option 4: 182.67 cm3
Correct Answer: 179.67 cm 3
Solution :
The diameter of the sphere is equal to the side of the cube.
d = 7 cm
r = $\frac{7}{2}$ cm
The volume of a sphere $= \frac{4}{3}\pi r^3$
$V = \frac{4}{3}\pi \left(\frac{7}{2}\right)^3 = \frac{4×22}{3×7}× \frac{343}{8} = 179.67$
Hence, the correct answer is 179.67 cm
3
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