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Geometry and Measurement Videos 87 videos

SAT Math 1.1 Geometry and Measurement
719 Views

SAT Math 1.1 Geometry and Measurement. What is the circumference of the circle?

SAT Math 1.2 Geometry and Measurement
246 Views

SAT Math: Geometry and Measurement Drill 1, Problem 2. If A = (0, 4), B = (-3, 2), and C = (1, 0), which point is in the interior of angle ABC?

SAT Math 1.3 Geometry and Measurement
231 Views

SAT Math 1.3 Geometry and Measurement. Find the length of CE.

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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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