Question

A truck that is 12 ft. by 10 ft. by 15 ft. carries cube

shaped boxes that have a length of 2 ft. How many
of these boxes can this truck hold?

Answer 1

Answer: 284 boxes in the shape of the cubes can be fitted in the truck.

Explanation:

If a truck is fitted fully with the cubes, volume of the truck will be equal to the volume of cubes to be fitted.

Dimensions of the truck given in the question,

Length = 10 feet, width = 12 feet and height = 8 feet

Since, volume of a cuboid (shape of a truck) is given by the expression,

Volume = Length × Width × Height

Therefore, volume of the truck = 10 × 12 × 8

= 960 feet³

Volume of a cube is given by the expression,

Volume = (side)³

Therefore, volume of the cube with side length 1.5 feet will be,

Volume of a cube = (1.5)³

= 3.375 cubic feet

Let the number of cubes fitted in the truck = x

Therefore, volume of 'x' cubes = (3.375x) feet³

Since, volume of the truck = Volume of the cubes fitted

3.375x = 960

x = 960/3.375

x = 284.44

x ≈ 284

Therefore, 284 boxes in the shape of the cubes can be fitted in the truck.

Answer 2

225 boxes

Explanation:

1. Calculate the volume of the container:

`v_(c) =(12)(10)(15)=1800ft^(3)`

2. Calculate the volume of the boxes:

`v_(b) =(2)^(3) =8ft^(3)`

3. Calculate the number of boxes that fit in the container:

`boxes=(1800)/(8) =225`

Hope this helps