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

Problem:
We are given the radius of a sphere as \( \frac{7}{2} \) cm, and we are asked to find the volume of the sphere.

Step 1: Recall the volume formula for a sphere
The volume \(V\) of a sphere is calculated using the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.

Step 2: Substitute the given radius into the formula
Given \( r = \frac{7}{2} \), substitute this into the volume formula:
\[ V = \frac{4}{3} \pi \left( \frac{7}{2} \right)^3 = \frac{4}{3} \pi \cdot \frac{343}{8} = \frac{1372}{24} \pi = \frac{343}{6} \pi \]
Now use the exact value of \( \pi = \frac{22}{7} \) for simplification:
\[ V = \frac{343}{6} \times \frac{22}{7} = \frac{343 \times 22}{6 \times 7} = \frac{7546}{42} = \frac{539}{3} \, \text{cm}^3 \]

Final Answer:
The volume of the sphere is \(\frac{539}{3}\) cubic centimeters.