Question

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

• A. \(\frac{231}{3}\) cu cm
• B. \(\frac{539}{12}\) cu cm
• C. \(\frac{539}{3}\) cu cm
• D. \(154\) cu cm

Answer 1

The Correct Option is C

The volume \(V\) of a sphere is given by the formula:

\[ V = \frac{4}{3} \pi r^3 \]

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

\[ V = \frac{4}{3} \pi \left(\frac{7}{2}\right)^3 = \frac{4}{3} \pi \times \frac{343}{8} \]

Simplifying:

\[ V = \frac{4 \times 343}{3 \times 8} \pi = \frac{1372}{24} \pi = \frac{343}{6} \pi \]

Approximating \(\pi \approx 3.14\):

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

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