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Area and Volume Videos 7 videos

SAT Math 1.4 Geometry and Measurement
224 Views

SAT Math 1.4 Geometry and Measurement. If the sides of a square increase in size by 25%, what happens to the area of the square?

SAT Math 1.5 Geometry and Measurement
215 Views

SAT Math 1.5 Geometry and Measurement. How many jars of paint will Sierra need?

SAT Math 6.5 Geometry and Measurement
198 Views

SAT Math 6.5 Geometry and Measurement

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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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