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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


Team Careers360 3rd Jan, 2024
Answer (1)
Team Careers360 19th Jan, 2024

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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