033 Review Problem - Finding which one is the better bargain

For oranges of 2-3/4 in. in diameter (radius = 1.375 in.)
Volume, $V_1 = 12 \times \frac{4}{3}\pi (1.375^3) = \frac{1331}{32}\pi ~ \text{in}^3$

Unit cost, $U_1 = \dfrac{15 ~ \text{cents}}{\frac{1331}{32}\pi ~ \text{in}^3} = 0.1148 ~ \text{cent/in}^3$
 

For oranges of 3-1/2 in. in diameter (radius = 1.75 in.)
Volume, $V_2 = 12 \times \frac{4}{3}\pi (1.75^3) = \frac{343}{4}\pi ~ \text{in}^3$

Unit cost, $U_2 = \dfrac{30 ~ \text{cents}}{\frac{343}{4}\pi ~ \text{in}^3} = 0.1114 ~ \text{cent/in}^3$
 

Thus, the 30 cents per dozen is the better bargain.           answer