Question

Melissa is stacking storage cubes in a crate the bottom of the crate is 8 inches by 12 inches. The volume of the crate is 768 cubic inches. If a storage cube has a length of 4 inches, how many storage cubes will fit in the crate?

Answer 1

Answer: 12 storage cubes will fit into Melissa's crate

Step-by-step explanation:

Melissa's crate is a cuboid. Since the crate has a bottom dimension of 8 inches by 12 inches, it is assumed that the width of the cuboid (crate) is 8 inches and the length of the cuboid is 12 inches.

Since the volume = 768 cubic inches, the length = ? inches

The volume of cuboid = length × width × height

768 = 12 × 8 × h

96 × h = 768

h = 768/96

h = 8 inches

The height of the cuboid is 8 inches.

Now, since each of the cubes being stacked into the crate has a side of 4 inches, the volume of each cube is therefore:-

Volume of a cube = L^3 (since all sides of a cube is equal)

Where L = length of a side of cube

Volume = 4 × 4 × 4

Volume = 64 cubic inches.

To calculate the quantity of storage cubes that can fit into the crate, we then divide the volume of the crate by the volume of the storage cube:

= 768/64

= 12

Therefore, 12 storage cubes will fit into the crate.

Answer 2

Answer:

12 cubes can fit in the create.

Step-by-step explanation:

We know that the volume of a the crate is 768 in³, and the definition of the volume is:

$V=A*h$

Where:

• V is the volume
• A is the area (A=8*12 in²)
• h is the height

So $h=\frac{V}{A}=\frac{768}{12*8}=8 in$    

Now, we know that the storage cube has a length of 4 in so we have a volume equal to 64 in³. Therefore we just need to divide 768 in³ by 64 in³ it is 12.

Finally, 12 cubes can fit in the create.

I hope it helps you!