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SAT Math 6.5 Geometry and Measurement 198 Views


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Description:

SAT Math 6.5 Geometry and Measurement

Language:
English Language

Transcript

00:02

Here’s your shmoop du jour, brought to you by a box that is two-thirds full.

00:07

Or, as we might look at it depending on our mood…one-third empty.

00:12

A rectangular box with a square base and a height of twice the length of the base, is

00:16

to be filled two-thirds of the way full. If x is the length of one side of the base,

00:22

what is the volume of the remaining space in the box?

00:26

Here are the potential answers...

00:29

Okay, so we’re not sure what exactly this box is filled with…

00:33

...all we know is that we recently saw someone carrying it out of the horses’ stable.

00:37

So…we’re not gonna ask. All right, now let’s picture this box.

00:41

Square base… but with a height twice the length of the base.

00:44

And it’s filled 2/3 of the way with… something.

00:48

We want to determine how much room we have leftover.

00:51

We’re calling a length of the square base “x”…

00:55

…and since we know the sides are twice as long as the base, we can call the height “2x.”

00:59

Now for the volume portion of the program…

01:01

We need to take length times width times height to get the volume.

01:06

Since we know the base is a square, both of those measurements are just…”x.”

01:11

So to find the volume, we take x times x times 2x…

01:15

…to get 2x cubed. But that’s the total volume of the box.

01:19

If only 1/3 of that is empty space…

01:21

…then we take 1/3 times 2x cubed to get 2/3x cubed…

01:26

…which is answer B.

01:28

We love problems like this. They really… fertilize the imagination…

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