To find the volume of a sphere when its total surface area and radius are given, follow these steps:

1. Calculate the radius:

Given that the total surface area (TSA) of the sphere is \( 154 \, \text{cm}^2 \) and the radius \( r = 3.5 \, \text{cm} \), use the formula for TSA:

\[
\text{TSA} = 4 \pi r^2
\]

\[
154 = 4 \pi (3.5)^2
\]

2. Verify the radius:

\[
(3.5)^2 = 12.25
\]

\[
\text{TSA} = 4 \pi \times 12.25 = 154
\]

\[
4 \pi \times 12.25 = 154
\]

\[
\pi = \frac{154}{49} \approx 3.1416
\]

3. Calculate the volume of the sphere:

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

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

Given \( r = 3.5 \, \text{cm} \):

\[
V = \frac{4}{3} \pi (3.5)^3
\]

\[
(3.5)^3 = 42.875
\]

\[
V = \frac{4}{3} \pi \times 42.875
\]

\[
V = \frac{4}{3} \times 3.1416 \times 42.875
\]

\[
V \approx 179.67 \, \text{cm}^3
\]

The correct answer is:

D. 179.67 cm³