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CAHSEE Math 4.3 Measurement and Geometry 186 Views


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Measurement and Geometry Drill 4 Problem 3. In the figure below, how many of the 3 inch cubes would fit into a rectangular block of ice with the dimensions as shown?

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Transcript

00:03

You look like you could use a shmoopy question…

00:07

Ivan is a Russian bartender with a particular affinity for nesting dolls.

00:11

He wants to apply the same idea to ice cubes.

00:14

The guy dreams big, what can we say?

00:17

In the figure below, how many of the 3 inch

00:19

cubes would fit into a rectangular block of ice with the dimensions as shown?

00:24

And here are the potential answers...

00:32

Tons of things going on here so let’s start by just standardizing units.

00:36

That is, making everything into inches instead of feet.

00:39

We can glean that the ice cube in the upper corner of the larger block of ice there is

00:43

one FOURTH of the way across because it is labeled 3 inches…

00:47

…and you can see that the front base is a foot – 12 inches.

00:51

Now since it’s an ice cube, the CUBE being the operative word here,

00:55

by definition all sides are the same length.

00:58

So this line is 3 inches as well and the side length of the bigger block of ice

01:02

is 1 and a quarter feet, or 15 inches.

01:06

The back side is 1 and a half feet, or 18 inches.

01:09

So let’s calculate the volume of the rectangular ice block by multiplying base times width

01:15

times height – all in inches - and we get 12 times 15 times 18 is 3,240.

01:24

So the volume of the rectangular block is 3,240 cubic inches.

01:30

Now we have to figure out how many 3 by 3 inch cubes can fit in there.

01:34

Well, the volume of these cubes is calculated the same way as the larger ice block –

01:39

base times height times width.

01:42

We have 3 times 3 which is 9… times 3 which is 27.

01:46

So to figure out how many cubes should fit into the larger chunk of ice, we divide 3,240 by 27...

01:58

Okay, there we go. And we get 120. The answer is D.

02:03

As in, “Don’t quit your day job.”

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