That gives a volume of 1241.59 cubic cm per orange.

4000 kg of oranges would be 30,534 oranges for a total volume of 38 cubic Meters. (and spheres won’t pack with 100% efficiency, so an even larger volume would be required to contain that many oranges.

Per US EPA standards, a mid size car has an interior volume between 3.11 and 3.37 cubic meters.

According to the picture, they only filled the back seat.

Because spheres don’t pack all that efficiently, you will get less than 800 oranges per cubic meter. Since only the back half of the passenger compartment of the car in the picture at the linked article is filled with oranges, they had at most, 1200 oranges (around 157 Kg)

The second car, being larger is still at most, another 4 cubic meters. And don’t forget, they can’t completely fill the cars as they need to leave room for a driver at a minimum.

That would mean that the van would have to be at least 31 cubic meters and probably closer to 35 cubic meters to make it work. A 28 foot semi trailer is only 57 cubic meters. The van pictured is a passenger van, not a cargo van, it might go as much as 12 cubic meters, but I doubt it.

I looked at the U-Haul web site. You’d need their largest size panel truck (26 ft) to get the requisite cargo volume. And it’s load weight limit is only 7400 pounds (3356 kg)

“Who knows as oranges around the world have different sizes.”

Different sizes wouldn’t affect the aggregate volume of a given mass of oranges that much unless there was significant variance in the individual density of the oranges. The smaller oranges would have less mass, so you need more of them to get the reported aggregate mass.

Sorry; I used to teach math, and your analysis has an obvious flaw. using 4/3 pi*r^3, where r = 3.34 cm, gives a volume of 156 cc. You got an answer 8 times this large because you used the diameter, and not the radius.

A quick engineering check. Assume the density of an orange to be about the density of water. 131 gm would be the equivalent of 131 cc of water. As an engineer would say, that’s within round-off error.

Now you get, according to the rest of your analysis, about 10,000 oranges in the car, or about 1300 kg. That would include the trunk as well as the back seat. The car would really have been dragging.

Oops, I completely missed that I used diameter where I should have used the radius.

It still comes to an aggregate volume of 4.74 cubic meters. There might be enough volume, but sill not near enough weight capacity even across three vehicles (the car, an SUV and a passenger van)

The pictures in the link at the linked article show the back seat of the car, the cargo area of the SUV and the back cargo area of the van (which wasn’t even packed full)

Great Unknown’ So true. Anyone raised with the metric system knows that 1g is roughly equal to 1 cubic cm of water.

In spite of the Metric Conversion Act, signed into law in 1975, the U.S. joins with Liberia and Myanmar as the only three countries to still use the Imperial system of weights and measures.

The U.S. Metric Society is a national non-profit organization that was founded in 1916. USMA advocates completing the US conversion to the International System of Units. There has been some progress; with the giant agriculture and building industries being most resistant.

## 8 Comments

There’s no Fifth Amendment in Spain. Orange you glad?

Something doesn’t add up here

According to this site, https://hannaone.com/Recipe/weightorange.html , the average weight for a medium orange is 131g and the average size is 2 5/8 inches (6.6675cm)

That gives a volume of 1241.59 cubic cm per orange.

4000 kg of oranges would be 30,534 oranges for a total volume of 38 cubic Meters. (and spheres won’t pack with 100% efficiency, so an even larger volume would be required to contain that many oranges.

Per US EPA standards, a mid size car has an interior volume between 3.11 and 3.37 cubic meters.

According to the picture, they only filled the back seat.

Because spheres don’t pack all that efficiently, you will get less than 800 oranges per cubic meter. Since only the back half of the passenger compartment of the car in the picture at the linked article is filled with oranges, they had at most, 1200 oranges (around 157 Kg)

The picture doesn’t tell the entire story MattS.

The linked BBC article shows there were two more cares including a large fleet type van.

Does that get you to the volume needed? Who knows as oranges around the world have different sizes.

The point is there were other vehicles other than the one in the original linked article.

“Does that get you to the volume needed?

Possibly, but I think probably not.

The second car, being larger is still at most, another 4 cubic meters. And don’t forget, they can’t completely fill the cars as they need to leave room for a driver at a minimum.

That would mean that the van would have to be at least 31 cubic meters and probably closer to 35 cubic meters to make it work. A 28 foot semi trailer is only 57 cubic meters. The van pictured is a passenger van, not a cargo van, it might go as much as 12 cubic meters, but I doubt it.

I looked at the U-Haul web site. You’d need their largest size panel truck (26 ft) to get the requisite cargo volume. And it’s load weight limit is only 7400 pounds (3356 kg)

“Who knows as oranges around the world have different sizes.”

Different sizes wouldn’t affect the aggregate volume of a given mass of oranges that much unless there was significant variance in the individual density of the oranges. The smaller oranges would have less mass, so you need more of them to get the reported aggregate mass.

It still doesn’t add up.

Sorry; I used to teach math, and your analysis has an obvious flaw. using 4/3 pi*r^3, where r = 3.34 cm, gives a volume of 156 cc. You got an answer 8 times this large because you used the diameter, and not the radius.

A quick engineering check. Assume the density of an orange to be about the density of water. 131 gm would be the equivalent of 131 cc of water. As an engineer would say, that’s within round-off error.

Now you get, according to the rest of your analysis, about 10,000 oranges in the car, or about 1300 kg. That would include the trunk as well as the back seat. The car would really have been dragging.

Oops, I completely missed that I used diameter where I should have used the radius.

It still comes to an aggregate volume of 4.74 cubic meters. There might be enough volume, but sill not near enough weight capacity even across three vehicles (the car, an SUV and a passenger van)

The pictures in the link at the linked article show the back seat of the car, the cargo area of the SUV and the back cargo area of the van (which wasn’t even packed full)

Dear Mr. Olson,

When can we expect a new domain and design on your new blogging adventure of “OverMathed?”

đŸ˜‰

Great Unknown’

So true. Anyone raised with the metric system knows that 1g is roughly equal to 1 cubic cm of water.

In spite of the Metric Conversion Act, signed into law in 1975, the U.S. joins with Liberia and Myanmar as the only three countries to still use the Imperial system of weights and measures.

The U.S. Metric Society is a national non-profit organization that was founded in 1916. USMA advocates completing the US conversion to the International System of Units. There has been some progress; with the giant agriculture and building industries being most resistant.