Question

You are working for a company that designs boxes, bottles and other containers. You are currently working on a design for a milk carton as shown alongside. The base is a square, 6 cm by 6 cm. The height of the carton is 10 cm. Four overlapping semi-circular flaps seal the top of the carton, each with a radius of 3 cm. The area of a circle is: A = r². Area of square= s², Area of rectangle = 1xb
1.1Find the volume of each milk carton in cm³. Use the formula V = 1x bx h.

1.2Determine how much cardboard (the area) is needed to make a single milk carton.

1.3How many litres of milk can each carton hold?

1.4What will it cost to fill 200 cartons with milk, if milk costs R1 200 per kilolitre? Assume that you can buy exactly as much milk as is needed (you don't have to purchase a whole kilolitre if you only need 10 litres, for example).​

Answer 1

Volume is a measure of the quantity of substance a given object can contain. The required answers are:

1.1  The volume of each milk carton is 360 $cm^{3}$.

1.2  The area of cardboard required to make a single milk carton is  332.6 $cm^{2}$.

1.3  Each carton can hold 0.36 liters of milk.

1.4  The cost of filling the 200 cartons is R 86.40.

The volume of a given shape is the amount of substance that it can contain in a 3-dimensional plane. Examples of shapes with volume include cubes, cuboids, spheres, etc.

The area of a given shape is the amount of space that it would cover on a 2-dimensional plane. Examples of shapes to be considered when dealing with the area include triangle, square, rectangle, trapezium, etc.

The box to be considered in the question is a cuboid. So that;

Volume of cuboid = length x width x height

Thus,

1.1 The volume of each milk carton = length x width x height

                                                         = 6 x 6 x 10

                                                        = 360

The volume of each milk carton is 360 $cm^{3}$.

1.2 The total area of cardboard required to make a single milk carton can be determined as follows:

i. Area of the rectangular surface = length x width

                                                    = 6 x 10

                                                    = 60

Total area of the rectangular surfaces = 4 x 60

                                                     = 240 $cm^{2}$

ii. Area of the square surface = side x side = s²

                                                   = 6 x 6  

 Area of the square surface = 36 $cm^{2}$

iii. There are four semicircular surfaces, this implies a total of 2 circles.

Area of a circle = $\pi r^{2}$

where r is the radius of the circle.

Total area of the semicircular surfaces = 2 $\pi r^{2}$

                                        = 2 x $\frac{22}{7}$ x $(3)^{2}$

                                        = 56.57

Total area of the semicircular surfaces = 56.6 $cm^{2}$

Therefore, total area of  cardboard required = 240 + 36 + 56.6

                                                            = 332.6 $cm^{2}$

The area of cardboard required to make a single milk carton is  332.6 $cm^{2}$.

1.3 Since,

  1 $cm^{3}$  = 0.001 Liter

Then,

360 $cm^{3}$ = x

x = 360 x  0.001

  = 0.36 Liters

Thus each carton can hold 0.36 liters of milk.

1.4 total cartons = 200

Total volume of milk required = 200 x 0.36

                                                 = 72 litres

But, 1 kiloliter costs R1 200. Thus

Total volume in kiloliters = $\frac{72}{1000}$

                                         = 0.072 kiloliters

The cost of filling the 200 cartons = R1200 x 0.072

                                         = R 86.40

The cost of filling the 200 cartons is R 86.40.

For more clarifications on the volume of a cuboid, visit: brainly.com/question/20463446

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