PLSS HELP!

You are working for a company that designs boxes, bottles and other containers. You are currently working on a design for a milk

ra1l [238]

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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