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:
A sphere has a radius of \( \frac{7}{2} \) cm. Determine the sphere's volume.

Step 1: State the sphere volume formula
The volume \(V\) of a sphere is given by:
\[V = \frac{4}{3} \pi r^3\]
where \( r \) represents the sphere's radius.

Step 2: Apply the formula with the given radius
Substitute \( r = \frac{7}{2} \) into the volume formula:
\[V = \frac{4}{3} \pi \left( \frac{7}{2} \right)^3= \frac{4}{3} \pi \cdot \frac{343}{8}= \frac{1372}{24} \pi= \frac{343}{6} \pi\]
Using the approximation \( \pi = \frac{22}{7} \) for calculation:
\[V = \frac{343}{6} \times \frac{22}{7} = \frac{343 \times 22}{6 \times 7} = \frac{7546}{42}= \frac{539}{3} \, \text{cm}^3\]

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