A sphere is placed in a cone of height $15.3\;cms$. The volume of the sphere if it touches the lateral surface and the base of the cone is _____ $cm^3$

Question

$(A) \; 1451\;\pi\;cm^3 \\(B)\;1514\;\pi \;cm^3 \\(C)\;1415 \; \pi \;cm^3 \\(D)\;1145 \pi \;cm^3$