Dimensions of a pack of 12 cans:
-length :29,2 cm
-Width : 21,9 cm
-height : 10,8 cm
The mass of an empty can is 40g.
The mass of a fully packed shipping crate with cans of fish is 280 kg.
The inner dimensions of a shipping crate are 117 cm by 66 cm by 50 cm.
Packs of cans are placed lengthwise (length to length) in the shipping crates.
Aggie states that an empty shipping crate has a mass of less than 20kg.
Verify,with calculations, if her statement is valid
117/29.2 = 4 packs lengthwise per crate
66/21.9 = 3 packs wide
50/10.8 = 4.62 packs high
so it looks like a crate can hold only 4*3*4 = 48 packs
That is 48*12 = 576 cans
you don't give the mass of a full can of fish, so there's no way to know how much of the 280kg is contents, and how much is just crate.
Well, Aggie seems to be underestimating the weight of an empty shipping crate, but let's do the math to verify.
First, we need to calculate the volume of the shipping crate. Using the inner dimensions given, the volume is:
Volume = Length x Width x Height
Volume = 117 cm x 66 cm x 50 cm
Volume ≈ 388,980 cm³
Next, we need to find the volume of a single can. Since the dimensions given are for a pack of 12 cans, we'll divide them by 12 to get the dimensions of a single can:
Length of a can = 29.2 cm / 12 ≈ 2.43 cm
Width of a can = 21.9 cm / 12 ≈ 1.82 cm
Height of a can = 10.8 cm / 12 ≈ 0.9 cm
Now we can calculate the volume of a single can:
Volume of a can = Length x Width x Height
Volume of a can ≈ 2.43 cm x 1.82 cm x 0.9 cm
Volume of a can ≈ 3.9846 cm³
Since there are 12 cans in a pack, we can multiply the volume of a single can by 12 to get the total volume of the pack:
Total pack volume = 3.9846 cm³ x 12 ≈ 47.8152 cm³
To fill the shipping crate lengthwise, we need to divide the crate's volume by the total pack volume:
Number of packs that fit lengthwise = Crate volume / Total pack volume
Number of packs that fit lengthwise ≈ 388,980 cm³ / 47.8152 cm³ ≈ 8,131.1021
Now, let's calculate the mass of a fully packed shipping crate with cans of fish. We know that the mass of an empty can is 40g, and there are 12 cans in a pack. So, the mass of a pack of cans is:
Mass of a pack of cans = Mass of an empty can x Number of cans
Mass of a pack of cans = 40g x 12 ≈ 480g
To convert the mass of the fully packed shipping crate from grams to kilograms:
Mass of fully packed shipping crate = 280 kg x 1000 = 280,000 g
Finally, let's calculate the total mass of the packs inside the shipping crate:
Total mass of packs inside crate = Mass per pack x Number of packs
Total mass of packs inside crate ≈ 480g x 8,131.1021 ≈ 3,910,127.878 g
Converting the total mass of the packs inside the crate from grams to kilograms:
Total mass of packs inside crate ≈ 3,910,127.878 g / 1000 ≈ 3910.128 kg
So, based on the calculations, the total mass of the packs inside the shipping crate is 3910.128 kg, which is significantly more than 20 kg. Therefore, Aggie's statement is not valid.
To verify Aggie's statement, we need to calculate the mass of the empty shipping crate and compare it to 20 kg.
First, let's calculate the volume of the shipping crate:
Volume = Length x Width x Height
Volume = 117 cm x 66 cm x 50 cm
Volume = 387,180 cm³
Since there are 12 cans in a pack, we also need to calculate the volume of one pack:
Volume of one pack = Length x Width x Height
Volume of one pack = 29.2 cm x 21.9 cm x 10.8 cm
Volume of one pack = 6,372.864 cm³
Now, let's calculate the number of packs that can fit in the shipping crate:
Number of packs = Volume of shipping crate ÷ Volume of one pack
Number of packs = 387,180 cm³ ÷ 6,372.864 cm³
Number of packs ≈ 60.775
Since we can't have a fraction of a pack, the maximum number of packs that can fit in the shipping crate is 60.
Next, we calculate the mass of the packs in the shipping crate:
Mass of packs = Mass of one pack x Number of packs
Mass of packs = 40 g x 60
Mass of packs = 2,400 g = 2.4 kg
Finally, let's calculate the total mass of the shipping crate:
Total mass = Mass of packs + Mass of the empty shipping crate
Total mass = 2.4 kg + 280 kg
Total mass = 282.4 kg
From the calculations, we can see that the total mass of the empty shipping crate (282.4 kg) is greater than 20 kg. Therefore, Aggie's statement that an empty shipping crate has a mass of less than 20 kg is not valid.
To verify Aggie's statement, we need to calculate the mass of the empty shipping crate using its dimensions and the mass of each pack of 12 cans.
First, let's calculate the volume of the shipping crate:
Volume = length x width x height
Volume = 117 cm x 66 cm x 50 cm
Next, let's calculate the volume of each pack of 12 cans:
Volume of pack = length x width x height
Volume of pack = 29.2 cm x 21.9 cm x 10.8 cm
Now, let's calculate the number of packs that can fit in the shipping crate:
Number of packs = (length of the shipping crate / length of each pack) x (width of the shipping crate / width of each pack) x (height of the shipping crate / height of each pack)
Number of packs = (117 cm / 29.2 cm) x (66 cm / 21.9 cm) x (50 cm / 10.8 cm)
Once we know the number of packs that can fit in the shipping crate, we can calculate the mass of the fully packed shipping crate:
Mass of fully packed shipping crate = mass of each pack x number of packs + mass of the empty shipping crate
Finally, we can compare the calculated mass of the fully packed shipping crate to 20 kg to verify Aggie's statement.
Let's do the calculations:
Volume of pack = 29.2 cm x 21.9 cm x 10.8 cm = 6597.984 cm³
Number of packs = (117 cm / 29.2 cm) x (66 cm / 21.9 cm) x (50 cm / 10.8 cm) ≈ 4 x 3 x 4 = 48 packs
Mass of fully packed shipping crate = mass of each pack x number of packs + mass of the empty shipping crate
Mass of fully packed shipping crate = (12 cans x 40 g) x 48 packs + 280,000 g = 16,320 g + 280,000 g = 296,320 g
Now let's convert grams to kilograms:
Mass of fully packed shipping crate = 296,320 g ÷ 1000 = 296.32 kg
Since the mass of the fully packed shipping crate is 296.32 kg, which is greater than 20 kg, Aggie's statement is not valid.