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Alexeev081 [22]
3 years ago
9

I need some help with this question

Mathematics
1 answer:
Tems11 [23]3 years ago
7 0

Check the picture below.

namely, is the volume of the rectangular prism Paraffin, equals or less than the volume of the cone made from it?

\bf  \textit{volume of a rectangular prism}\\\\ V=Lwh~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=8\\ w=6\\ h=4 \end{cases}\implies V=8\cdot 6\cdot 4\implies \boxed{V=192} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=25 \end{cases}\implies V=\cfrac{\pi (5)^2(25)}{3}\implies \boxed{V\approx 654.5}

well, clearly the cone has enough room to take the 192 cm³.

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D. A over 4

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A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 7.5 ft
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Considering the definition of right rectangular prism and its volume,  the total weight of the contents is 38.81 pounds.

<h3>Right rectangular prism</h3>

A right rectangular prism (or cuboid) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.

<h3>Volume of right rectangular prism</h3>

To calculate the volume of the rectangular prism, it is necessary to find the product of its dimensions, or of the three edges that converge at a certain vertex.

That is, to calculate the volume of a rectangular prism, multiply its 3 dimensions: length×width×height.

<h3>Volume of the container </h3>

In this case, you know that:

  • the dimensions of the container built are 7.5 ft by 11.5 ft by 3 ft.
  • the container is entirely full and, on average, its contents weigh 0.15 pounds per cubic foot.

So, the volume of the container is calculated as:

7.5 ft× 11.5 ft× 3 ft= <u><em>258.75 ft³</em></u>

Then, the total weight of the contents is calculated as:

258.75 ft³×  0.15 pounds per cubic foot= <u><em>38.8125 pounds≅ 38.81 pounds</em></u>

Finally, the total weight of the contents is 38.81 pounds.

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