## 283. Math Puzzle $12 / 88$

Robert knows that his younger brother loves to eat oranges. That's why he wants to give him an orange gift for Christmas. In the vegetable store, he sees a super specimen of this fruit: $12 \mathrm{~cm}$ in diameter! The peel, however, is $1 \mathrm{~cm}$ thick.

Now he wonders if his brother will get more of it if he packs 7 oranges instead of the large one, each with a diameter and peel that are exactly half as large or thick as the giant piece.

The saleswoman assures him that the oranges are uniformly spherical and of the same quality.

What does Robert decide to do to give his brother the larger amount of fruit flesh?
The volume (pulp) of the large tangerine is

$$
V=\frac{1}{6} \pi d^{3}=\frac{1}{6} \pi \cdot 10^{3} \mathrm{~cm}^{3}=523.6 \mathrm{~cm}^{3}
$$

Seven small tangerines have a total volume of:

$$
V=7 \cdot \frac{1}{6} \pi 5^{3} \mathrm{~cm}^{3}=458.1 \mathrm{~cm}^{3}
$$

Robert, being a math enthusiast, will choose the large tangerine, as it contains more pulp than the seven small ones combined.