Question : Find the volume of the largest possible sphere circumscribed by a cube of edge 7 cm.
Option 1: 179.67 cm3
Option 2: 169.67 cm3
Option 3: 189.67 cm3
Option 4: 199.67 cm3
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Correct Answer: 179.67 cm 3
Solution :
Given: Side of the cube = 7 cm
Thus, the diameter of the sphere = 7 cm
Radius of sphere = $\frac{7}{2}$ cm.
Volume of the sphere = $\frac{4}{3}\pi r^3$
= $\frac{4}{3}×\frac{22}{7}×\frac{7}{2}×\frac{7}{2}×\frac{7}{2}$
= $\frac{49×11}{3}$ = $\frac{539}{3}$ = 179.67 cm
3
Hence, the correct answer is 179.67 cm
3
.
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