Explanation:

- A sphere and a cylinder have the same radius. The sphere is melted and reshaped into the cylinder, which means they have the same volume.

- Volume of a sphere: \( \frac{4}{3} \pi r^3 \).

- Volume of a cylinder: \( \pi r^2 h \).

- Setting the volumes equal: \( \frac{4}{3} \pi r^3 = \pi r^2 h \).

- Solving for height \( h \): \( h = \frac{4}{3}r \).

- Total Surface Area of sphere: \( 4 \pi r^2 \).

- Total Surface Area of cylinder: \( 2\pi r h + 2\pi r^2 \).

- Substitute \( h \) with \( \frac{4}{3}r \) gives: \( 2\pi r (\frac{4}{3}r) + 2\pi r^2 = \frac{8}{3} \pi r^2 + 2\pi r^2 = \frac{14}{3} \pi r^2 \).

- Ratio of total surface area of sphere to cylinder: \(\frac{4 \pi r^2}{\frac{14}{3} \pi r^2} = \frac{12}{14} = \frac{6}{7} \).

- So, the ratio is 6 : 7.

- Answer: Option 4 ?