a 250 ml container of fruit drink measures 6.5cm by 4cm by 10cm. the tcarton manufacturer would like to do design a 1L box with each dimension ofincreased by the same amount. What are the...

a 250 ml container of fruit drink measures 6.5cm by 4cm by 10cm. the tcarton manufacturer would like to do design a 1L box with each dimension of

increased by the same amount. What are the dimensions of this larger container?

 

please write how did you solve it
thank's

Expert Answers
hala718 eNotes educator| Certified Educator

The volume for the small container (V1) = 250 ml

Now we need to exapnd the volume for the larger comtainer by 4 times==> V2 = 1 L = 1000 ml

Then dimensions for the small comtainer are:

6.5 *4 *10 = 260 cm^3 = 260 ml    ( 1 cm^3 = 1 ml)

For the larger container we need to expand it by the same ratio.

==> the dimensions for the larger container are:

(6.5)x *(4)x * 10x = 260*x^3  cm^3

Now the volume of the larger cartoon we need should be equal or a little larger than 1 litre (1000 ML)

==> 260x^3 = 1000

==> x^3 = 1000/260

==> x= 1.57 (approx.)

So x= 1.57 is the minimum amount that we will expand the cartoon's dimension so it will contain 1000ml (1 L).

Then the new dimensions are:

(6.5 * 1.57 ) *( 4*1.57) * (10* 1.57) = 1006.17 cm^3

= 10.205 * 6.28 * 15.7 = 1006.17 cm^3 

 

 

neela | Student

If the volume is increased by the same amount, then the designed volume is 250ml+250ml = 500ml. Then the tarcton has to increase the dimensions by a factor x. So the container dimension is 6*6x, 4x and 10x.

Since both shapes are similar,the volumes 250 ml and 500 ml  are proportional to the measures 6.5 by 4 by 6.5x by 4x by 10x

 250 ml =k*6.5*4*10..........(1) and

500ml = k(6.5x)(4x)(10x).........(2)., where k is the constant of proportionality.

We eliminate k  by dividing eq (1) by eq (2):

250/500 = k6.5*4*10/(k*6.5x*4x*10x)

1/2 = 1/x^3

Nultiply by 2x^3.

x^3 = 2

x = 2^(1/3) = 1.25992105

Therefore the  dimensions to be designed by the manufacturer =

(6.5x , 4x , 10x) = 8.195 , 5.0397 , 12.5992)