6) A balloon vendor has two identical helium tanks and small and large balloons. He uses all of the first tank to inflate 80 small balloons, all at the same pressure. Given that the large balloons, when inflated, have the same shape and pressure as the small ones, but a surface area 4 times larger, how many large balloons can he fill with the second tank?
(A) 10
(B) 16
(C) 20
(D) 24
(E) 40.
6) The answer is (A). If a body is elongated (maintaining proportions) by a factor of $n$, its external surface increases by a factor of $n^{2}$ and its volume by a factor of $n^{3}$. Therefore, since the large balloons have a surface area 4 times that of the small balloons, they have been dilated by a factor of 2 and thus their radius is double $(\sqrt{4}=2)$ that of a small balloon. Therefore, the volume of a large balloon is $2^{3}=8$ times that of a small balloon. Since the large balloons are inflated at the same temperature and pressure as the small balloons, the amount of gas needed to inflate a large balloon is 8 times that needed to inflate a small balloon. Therefore, the vendor can inflate only $\frac{80}{8}=10$ large balloons with the second tank.