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## CAHSEE

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# CAHSEE practice: Problems 35-37

## Video transcript

Problem 35. In the figure below, every
angle is a right angle. So they're just saying that's a
right angle, that's a right angle, these are all
right angles. You get the idea. What is the area, in square
units, of the figure? So the area. How can we figure this out? We can divide this up into a
bunch of rectangles and figure out their respective areas. So if we drew a rectangle right
here, that rectangle, what's its area? It's going to be 6 times
8, which is 48. That's that rectangle right
there, is 48 square units. Let's see what else we can do. We can do this rectangle
right here. That rectangle right there is
also 6 by 8, so this is also going to be 48 square
units right there. And then we have-- we'll
do it in another color. We have this rectangle-- that
rectangle right there is divided right there-- we have
this rectangle right here, which is 3 by 4. So 3 times 4 is 12 units. And then you have this
rectangle right here, which is 3 by 4. So it's also 12 square units. So the whole area of the entire
thing is 12 plus 48, which is 60. Right? 2 plus 48 is 50, right,
that's 60. So you have 60 there, and then
you have another 48, gives you 108, plus 12, which is 120. So the area in square units
of the figure is 120. Problem 36. A rectangular field is 363 feet
long and 240 feet wide. How many acres is the field? So let me draw this field. I'll do it in green because
we're talking about a field. So it is 363 feet long
and 240 feet wide. That's the dimensions
of the field. So if we wanted to do it in
square feet, we would multiply these two numbers. So how many square feet is it? Well, I'll do it out here. I'll do it on the left. So let me multiply it out. We have 240 times 363. Actually, I want to do it with
a little bit more space. So we're going to
do it in blue. Maybe I should do it here. I don't think it will
confuse you. So I have 240 times 363. 3 times 0 is 0. 3 times 4 is 12. Carry the 1. 3 times 2 is 6, plus 1 is 7. So it's 720. We can ignore that
for a little bit. Throw a 0 down here. 6 times 0 is 0. 6 times 4 is 24. 6 times 2 is 12, plus
this 2 is 14. And then we have our last
row to deal with. So we're going to add two 0's
because we're dealing with the hundreds place. 3 times 0 is 0. 3 times 4 is 12. This was 4, carry the 1. 3 times 2 is 6, plus 1 is 7. And now we can just
add everything up. 0. 2. 7 plus 4 is 11. Carry the 1. 1 plus 4 is 5. 5 plus 2 is 7. And then we have
1 plus 7 is 8. So the field is 87,120
square feet. Now, they want to know how
many acres is the field? And they say an acre
is 43,560. And you see all your choices
are whole numbers. And you can just eyeball this,
that 87,000 whatever is roughly twice 43,560. Right? 80,000 is roughly
twice 40,000. If you wanted to just hand-wave
it, you could just say, well, that's just
choice number A, or that's just 2, right? This looks like 2 times that. And if you wanted to verify it,
2 times-- let's verify it. Let me do it in a color that
you can actually see. So 43,560-- you wouldn't
actually have to do this on the test, but I want to
show you that our approximation works. 2 times 0 is 0. 2 times 6 is 12. 2 times 5 is 10, plus
the 1 is 11. 2 times 3 is 6, plus 1 is 7. 2 times 4 is 8. And we've got the exact number
which was the square footage of the field. So it's 2 acres. So if you do it like
that, it's 2 acres. 1 acre and 2 acres,
just like that. 37. The object below is made of 10
rectangular prisms-- that just means these three-dimensional
rectangular things-- each with dimensions of 5 centimeters
by 3 centimeters by 2 centimeters. What is the volume, in cubic
centimeters, of the object? So it's kind of this
plus sign, or this cross looking thing. And they do this-- I mean, these
things are really just to throw you off. So what is the volume
of each of these little cubes right there? So its volume is 5
times 2 times 3. So each cube has a volume
of, what's 5 times 2? Is 10, times 3 is 30. So each has 30 cubic
centimeters. Do it in a darker color. Each of these is 30
cubic centimeters. And how many of these are
there in this structure? Well, we have 2 layers. The top layer has 1 box here,
that's 1, 2-- this is the second box-- 2, 3,
4, and then 5. So the top layer has 5
in this plus sign. I could draw it like this. 1, 2, 3, 4, 5. So if we have 5 in the top
layer, and we have 2 layers. So we have 10 of these
boxes, right? So 10 boxes, or rectangular
prisms if you want to call it that, times 30 cubic centimeters
per box. The boxes cancel out, you get 10
times 30 cubic centimeters, and you get 300 cubic
centimeters is the volume of this entire structure. And that is choice D. I literally think they drew
these little diagonals just to confuse you, just to maybe make
you think that you have to do something with
triangles. But no, you just have to count
the number of boxes and figure out the volume of
each of them. We had 10 boxes, each of them
has a volume of 30 cubic centimeters, so 300 cubic
centimeters total.