Question

A candy company is designing the packaging for its new candy bar. The bars will be packed in cartons which are 1 foot wide, 1 foot high, and 1 foot long. How many of these cartons can they pack into the shipping crate which is 5 ft long, 12 ft wide, and 4 ft high?

show your work.

Answer 1

number of cartons that can be packed in the shipping crate = 240 cartons

Explanation:

The cartons are cube since the face all have the same dimension . The length = 1 ft, width = 1 ft and height = 1 ft.

The shipping crate is a rectangular prism or cuboid . The dimension is given as follows.

length = 5 ft

width = 12 ft

height = 4 ft

The number of the cartons that can be packed in the shipping crate can be calculated as follows.

volume of the cubed carton = L³

where

L = length

volume of the cubed carton = 1³ = 1 ft³

Volume of the shipping crate = LWH

where

L = length

W = width

H = height

Volume of the shipping crate = 5 × 12 × 4

Volume of the shipping crate = 240 ft³

number of cartons that can be packed in the shipping crate = 240/1 = 240 cartons

Answer 2

240 cartons

Explanation:

If the bars will be packed in cartons which are 1 foot wide, 1 foot high, and 1 foot long, the volume of the carton will be expressed as shown;

Volume of carton = Length * Breadth * Height

Volume of carton = 1ft*1ft*1ft

= 1ft³

Given the dimension of shipping crate to be 5 ft long, 12 ft wide, and 4 ft high, the volume of the tank will be 5*12*4 = 240ft³

Number of cartons they pack into the shipping crate = Volume of the shipping crate/volume of one carton

Number of cartons they pack into the shipping crate = 240ft³/1ft³

= 240 cartons