Question

A company sells cereals in boxes which measure 10 cm by 25 cm by 35 cm.

They make a special edition box which is mathematically similar to the original box.

The volume of the special edition box is 15 120cm .
Work out the dimensions of this box.

Answer 1

V = 12cm×30cm×42cm

Explanation:

Given the dimension of original box to be 10 cm by 25 cm by 35 cm.

Volume of the box = length × breath ×height

V = 10×25×35

V = 8150

If they make a special edition box which is mathematically similar to the original box, then we can generalise the volume of the original box by writing it in terms of a constant k

V = 10k×25k×35k...1

V = 8750k³ cm³

Given the Volume of the special edition box to be 15,120cm³ which bus similar to the volume of the original box, then

15,120 = 8750k³

k³ = 15,120/8750

k³ = 1.728

k = 1.728^1/3

k = 1.2

The dimension of the special edition box will be gotten by substituting k = 1.2 into eqn 1

V = 10(1.2)×25(1.2)×35(1.2)

V = 12cm×30cm×42cm

Answer 2

The dimensions of the special edition box are:

12cm by 30cm by 42cm

Explanation:

Given dimensions of original box:

10 cm by 25 cm by 35 cm

Hence, a = 10 cm; b = 25 cm; c=35cm.

Therefore, volume of box, V= a*b*c

V = 10cm*25cm*35cm =8750cm³

Since the original box and the special edition box are similar but the volume of the special edition box is 15 120 cm, to find the dimensions of the special box we have:

Lets take the volume as:

V = Xa*Xb*Xc

15120cm = 10X*25X*35X=

15120 = 8750X³

`X^3 = (15120)/(8750)`

X³ = 1.728

X = ³/1.728

X = 1.2

Let's substitute 1.2 for X, we have:

10(1.2) * 25(1.2) * 35(1.2) =

12 * 30 * 42

Therefore the dimensions of the special edition box =

12cm by 30cm by 42cm