Volume of sphere can be calculated as:
[tex]V= \frac{4}{3} \pi r^{3} [/tex]
Original Radius = 3 cm
So,
Original Volume will be:
[tex]V= \frac{4}{3} \pi (3)^{3}=36 \pi [/tex] cm³
Andy spent 4 seconds adding more snow which increased the radius by 0.25 cm per second. So total increase in the radius will be 4 x 0.25 = 1 cm
New radius = 4 cm.
New volume will be:
[tex]V= \frac{4}{3} \pi (4)^{3}= \frac{256 \pi }{3} [/tex] cm³
Ratio of current volume to original volume will be:
[tex] \frac{ \frac{256 \pi }{3} }{36 \pi } \\ \\
= \frac{64}{27} [/tex]
Therefore, the correct answer to this question is option D
