Question

A shipping box in the shape of a cube has edge lengths of 6 inches. It can hold 24 staplers.

If the dimensions of a shipping box are all doubled, how many staplers can the larger box hold?

24 staplers
48 staplers
96 staplers
192 staplers

Answer 1

`\huge\boxed{\sf 192 \ staplers}`

Explanation:

Formula to be used:

• Volume of a cube = Length³

`\rule[225]{225}{2}`

Solution:

Volume of the smaller cube:

Length = 6 in.

So,

Volume = (6)³

Volume = 216 in.³

Volume of the larger box:

Length = 6 × 2 = 12 in.

Volume = (12)³

Volume = 1728 in.³

From the question:

216 in.³ = 24 staplers

Using unitary method.

• Divide both sides by 216

1 in.³ = 24/216 staplers

1 in.³ = 0.11 staplers

• Multiply both sides by 1728

1728 in.³ = 0.11 × 1728

1728 in.³ = 192 staplers

So, a box with a volume of 1728 in.³ can hold 192 staplers.

`\rule[225]{225}{2}`

Answer 2

The larger box holds 192 staplers.

Explanation:

Given:

For Original box

A shipping box is a cube.

Wdge length = 6 inches

No. of staplers smaller box= 24 stablers

Now,

`\sf Volume = length^3 =6^3 = 216 in^3`

When the dimensions of a shipping box are all doubled

For Larger box.

length will be = 6*2 = 12 in

`\sf Volume = length^3 =12 ^3 = 1728in^3`

Now, let's calculate how many staplers the larger box can hold:

`\boxed{\textsf{No, of staplers in larger box } = \frac{\textsf{Volume of larger box}}{\textsf{Volume of original box}}*\textsf{No. of staplers in original box}}`

`\sf \textsf{No. of staplers inlarger box = }(1,728 )/(216 )*24`

`\sf \textsf{No. of staplers inlarger box = } 8 * 24 = 192 staplers.`

Therefore, the correct answer is 192 staplers.