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. \(\frac{343}{6}\) cu cm
• D. \(154\) cu cm

Answer 1

The Correct Option is C

Step 1: Understand Sphere Volume Formula:
The volume \(V\) of a sphere is calculated using the formula:
\[V = \frac{4}{3} \pi r^3\]where \(r\) denotes the sphere's radius.

Step 2: Substitute Radius and Calculate Volume:
Given the radius \( r = \frac{7}{2} \) cm, substitute this into the volume formula:
\[V = \frac{4}{3} \pi \left( \frac{7}{2} \right)^3\]Calculate the cube of the radius:
\[\left( \frac{7}{2} \right)^3 = \frac{7^3}{2^3} = \frac{343}{8}\]Substitute this value back into the volume equation:
\[V = \frac{4}{3} \pi \times \frac{343}{8}\]Simplify the expression:
\[V = \frac{4 \times 343}{3 \times 8} \pi = \frac{1372}{24} \pi\]Reduce the fraction \( \frac{1372}{24} \):
\[\frac{1372}{24} = \frac{343}{6}\]Therefore, the sphere's volume is:
\[V = \frac{343}{6} \pi \, \text{cm}^3\]

Step 3: Final Result:
The calculated volume of the sphere is \( \frac{343}{6} \pi \) cubic centimeters.