Two spherical cantaloupes of the same kind are sold at a fruit and vegetable stand. The circumference of one is 60 cm and that of the other is 50 cm. The larger melon is 1 1/2 times as expensive as the smaller. Which melon is the better buy and why?

change C to radius. C=2PI r
r= C/2PI
Now volume is 4/3 PI r^3

ratio of circumference: 60/50 = 1.2

ratio of volumes: 1.2^3 = 1.728
ratio of costs: 1.5

so, since volume has gone up more than cost, the larger is a better buy.

Of course, the thickness of the rind will also be a factor. Good luck - gotta buy it before you can cut it open.

Extra credit: what rind thickness (as a % of diameter) will make them equal value?

To determine which melon is the better buy, we need to compare their volumes since the volume represents the amount of fruit we get for our money.

First, let's find the radius of each cantaloupe using the circumference formula:

For the larger cantaloupe with a circumference of 60 cm:
Radius = Circumference / (2 * π) = 60 cm / (2 * 3.14) ≈ 9.55 cm

For the smaller cantaloupe with a circumference of 50 cm:
Radius = Circumference / (2 * π) = 50 cm / (2 * 3.14) ≈ 7.96 cm

Now, let's calculate the volume of each melon using the formula for the volume of a sphere:

Volume = (4/3) * π * r^3

For the larger cantaloupe:
Volume = (4/3) * π * (9.55 cm)^3 ≈ 3250.92 cm^3

For the smaller cantaloupe:
Volume = (4/3) * π * (7.96 cm)^3 ≈ 1683.24 cm^3

Next, let's compare the volumes:

The larger cantaloupe has a volume of approximately 3250.92 cm^3, while the smaller cantaloupe has a volume of approximately 1683.24 cm^3.

Since the larger cantaloupe has a greater volume, it means we get more fruit for our money.

However, we also know that the larger melon is 1 1/2 times as expensive as the smaller melon. So, we need to factor in the price difference as well.

If the price difference is less than 1.5 times, it means the larger cantaloupe is a better buy because although it costs more, the extra fruit we get justifies the additional cost.

On the other hand, if the price difference is more than 1.5 times, then the smaller cantaloupe is the better buy even though we get less fruit, because the price difference outweighs the volume difference.

To make the final decision, we need to know the actual prices of the cantaloupes.