Question

Cindy works at Jurassic Park and has been tasked to design a container in the shape of a rectangular prism for the incoming baby dinosaurs. The scaled model of the container has dimensions 2m by 4m by 6m. Cindy has decided to increase each dimension of the scaled model by the same amount in order to produce a container with a volume of 84 times the volume of the scale model. By what amount should Cindy increase each dimension of the scaled model?

Answer 1

The amount Cindy should increase in each dimension of the scaled model is 12 m.  

What is a rectangular prism?

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape. It is also called a cuboid.

We have:

The scaled model of the container has dimensions 2m by 4m by 6m.

Volume of the scaled model = 2×4×6 = 48 cubic m

Let x be the amount by which each dimension is increased.

(2 + x)(4 + x)(6 + x) = 84(48)

$\rm 48+44x+12x^2+x^3=4032$

$\rm x^3+12x^2+44x-3984=0$

$\rm x-12=0\quad \mathrm{or}\quad \:x^2+24x+332=0$

The quadratic equation has no real solution so,

x = 12 m

Thus, the amount Cindy should increase in each dimension of the scaled model is 12 m.  

Learn more about the rectangular prism here:

brainly.com/question/21308574

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