Sam and lauren are going on a date. For dinner, their options are thai or italian, then they will either go to a movie, go ice s
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Volume is a measure of the <u>quantity </u>of <em>substance</em> a given <u>object</u> can contain. The required answers are:
1.1 The <u>volume</u> of each <u>milk</u> carton is 360 .
1.2 The area of <em>cardboard</em> required to make a single <u>milk</u> carton is 332.6 .
1.3 Each <u>carton</u> can hold 0.36 liters of <u>milk</u>.
1.4 The <em>cost</em> of filling the 200 <u>cartons</u> is R 86.40.
The <u>volume</u> of a given <u>shape</u> is the amount of <em>substance</em> that it can contain in a 3-dimensional <em>plane</em>. Examples of <u>shapes</u> with volume include cubes, cuboids, spheres, etc.
The <u>area</u> of a given <u>shape</u> is the amount of <em>space</em> that it would cover on a 2-dimensional <em>plane</em>. Examples of <u>shapes</u> to be considered when dealing with the area include triangle, square, rectangle, trapezium, etc.
The box to be considered in the question is a <u>cuboid</u>. So that;
<u>Volume</u> of <u>cuboid</u> = length x width x height
Thus,
1.1 The <u>volume</u> of each <u>milk</u> carton = length x width x height
= 6 x 6 x 10
= 360
The <u>volume</u> of each <u>milk</u> carton is 360 .
1.2 The <em>total area</em> of<em> cardboard </em>required to make a single<u> milk</u> carton can be determined as follows:
i. <u>Area</u> of the <u>rectangular</u> surface = length x width
= 6 x 10
= 60
Total <u>area</u> of the <u>rectangular</u> surfaces = 4 x 60
= 240
ii. <u>Area</u> of the <u>square</u> surface = side x side = s²
= 6 x 6
<u>Area</u> of the <u>square</u> surface = 36
iii. There are four <em>semicircular</em> <u>surfaces</u>, this implies a total of 2 <u>circles</u>.
<em>Area</em> of a <u>circle</u> =
where r is the <u>radius</u> of the <u>circle</u>.
Total <u>area</u> of the <em>semicircular</em> surfaces = 2
= 2 x x
= 56.57
Total <u>area</u> of the <em>semicircular</em> surfaces = 56.6
Therefore, total area of <em>cardboard</em> required = 240 + 36 + 56.6
= 332.6
The <u>area</u> of <em>cardboard</em> required to make a single <em>milk carton</em> is 332.6 .
1.3 Since,
1 = 0.001 Liter
Then,
360 = x
x = 360 x 0.001
= 0.36 Liters
Thus each<em> carton</em> can hold 0.36 liters of <u>milk</u>.
1.4 total cartons = 200
<em>Total volume</em> of <u>milk </u>required = 200 x 0.36
= 72 litres
But, 1 kiloliter costs R1 200. Thus
<em>Total volume</em> in kiloliters =
= 0.072 kiloliters
The <u>cost</u> of filling the 200 cartons = R1200 x 0.072
= R 86.40
The <u>cost</u> of filling the 200 <u>cartons</u> is R 86.40.
For more clarifications on the volume of a cuboid, visit: brainly.com/question/20463446
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