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. Helena wants to build a plant stand like the one

shown, and she wants to find its volume. Draw
line(s) to show how she might divide the stand
into two or more sections to make finding the
volume easier.
Find the volume of each section you identified.
Then find the total volume of the stand. Explain.

. Helena wants to build a plant stand like the one shown, and she wants to find its-example-1
User Vidhi Dave
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1 Answer

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Answer: First section: (x³+x²-x-1); Second section: (2x³-6x+4); Total volume: (3x³+x²-7x+3)

Explanation:

The picture I attached was the lines I drew to make finding the volume easier.

To find the second upper side I subtracted x+1 from 2x+3, which came to x+2.

This is why I scrapped out the 2x+3 in the bottom to make it less confusing.

Now you should be able to separate the two prisms.

For the first section, multiply (x+1)(x+1)(x-1). I'll do the right two first because it's easier.

(x+1)(x²-1x+1x-1) -1x and 1x cancel out. So now it's (x+1)(x²-1).

The volume of the first section is (x³+x²-x-1).

For the second section, multiply (x+2)(2x-2)(x-1).

The first two turn out as (2x²-2x+4x-4), which is (2x²+2x-4). Then, multiply all that by (x-1): (2x²+2x-4)(x-1).

You should get (2x³-2x²+2x²-2x-4x+4), which is then (2x³-6x+4).

So the volume of the second section is (2x³-6x+4).

Then it asks you to find the total volume, so just add the two volumes: (x³+x²-x-1) + (2x³-6x+4). Then add like-terms.

(3x³+x²-7x+3) should be the total volume.

For the explaining part (being pretty vague), just say how the volumes for both sections were added by like-terms to sum up to the total volume of the plant stand.

Hope that had helped (or at least worked) :p

. Helena wants to build a plant stand like the one shown, and she wants to find its-example-1
User Narancs
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