A giant box has the dimensions of 1.5m x
0.75m x 0.6m. It stores smaller boxes with
dimensions of 5cm x 3cm x 4cm. If each
smaller box weighs 500g, and the big box
weighs 6000 kg when it is full, how much does
it weigh when it is empty?
To find the weight of the big box when it is empty, we need to subtract the weight of the smaller boxes from the total weight when it is full.
1. First, let's calculate the volume of the big box:
Volume of the big box = length x width x height
Volume = 1.5m x 0.75m x 0.6m (convert cm to m, so it will be 150cm x 75cm x 60cm)
Volume = 6750 cm³
2. Next, let's calculate the volume of each smaller box:
Volume of the smaller box = length x width x height
Volume = 5cm x 3cm x 4cm
Volume = 60 cm³
3. Now, let's calculate how many smaller boxes can fit into the big box:
Number of smaller boxes = Volume of the big box / Volume of each smaller box
Number of smaller boxes = 6750 cm³ / 60 cm³
Number of smaller boxes = 112.5
4. Since we cannot have a fraction of a box, we need to round down to the nearest whole number. Therefore, the big box can hold 112 smaller boxes.
5. Now, let's calculate the weight of all the smaller boxes:
Weight of all smaller boxes = Number of smaller boxes x Weight of each smaller box
Weight of all smaller boxes = 112 x 500g
Weight of all smaller boxes = 56,000g
6. Finally, let's calculate the weight of the big box when it is empty:
Weight of the big box when empty = Total weight when full - Weight of all smaller boxes
Weight of the big box when empty = 6000kg - (56,000g / 1000)kg (convert grams to kilograms)
Weight of the big box when empty = 6000kg - 56kg
Weight of the big box when empty = 5944kg
Therefore, the big box weighs 5944 kg when it is empty.