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).