Question:

The radius of a sphere is 72\frac{7}{2} cm. The volume of the sphere is:

Updated On: Dec 12, 2024
  • 2313\frac{231}{3} cu cm
  • 53912\frac{539}{12} cu cm
  • 5393\frac{539}{3} cu cm
  • 154154 cu cm
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The Correct Option is C

Solution and Explanation

The volume VV of a sphere is given by the formula:

V=43πr3 V = \frac{4}{3} \pi r^3

Substitute the radius r=72r = \frac{7}{2} cm into the formula:

V=43π(72)3=43π×3438 V = \frac{4}{3} \pi \left(\frac{7}{2}\right)^3 = \frac{4}{3} \pi \times \frac{343}{8}

Simplifying:

V=4×3433×8π=137224π=3436π V = \frac{4 \times 343}{3 \times 8} \pi = \frac{1372}{24} \pi = \frac{343}{6} \pi

Approximating π3.14\pi \approx 3.14:

V3436×3.14=179.39cu cm V \approx \frac{343}{6} \times 3.14 = 179.39 \, \text{cu cm}

The exact answer is 5393\frac{539}{3} cu cm, which matches option (C).

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