First, given a sphere of radius {{MATH_10}}, recall the formula for its volume, {{MATH_11}}. {{MATH_12}} {{CMD_13}} Similarly, recall that the surface area {{MATH_14}} of a sphere of radius {{MATH_15}} is given by {{MATH_16}} {{CMD_17}} Since the meteorite burns up radially at a rate proportional to its surface area {{MATH_18}} with constant of proportionality {{MATH_19}}, {{MATH_20}} {{CMD_21}} Now compute {{MATH_22}} and express it in terms of the surface area {{MATH_23}} and {{MATH_24}}. (If you {{CMD_25}}must{{CMD_26}} enter a derivative of the function {{MATH_27}} with respective time, simply write {{MATH_28}}, not {{MATH_29}} {{MATH_30}} {{CMD_31}} Equating these two expressions obtained for {{MATH_32}}, we find that {{MATH_33}}. If the meteorite is still burning up at a time {{MATH_34}}, then {{MATH_35}}. Therefore for such {{MATH_36}}, {{MATH_37}} Thus, {{MATH_38}} is constant. {{CMD_39}} {{CMD_40}} {{CMD_41}} {{CMD_42}} {{CMD_43}} {{CMD_44}}