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Course: Digital SAT Math > Unit 13
Lesson 1: Area and volume: advancedVolume word problems — Basic example
Watch Sal work through a basic Volume word problem.
Want to join the conversation?
- what is the formula of volume?(6 votes)
- are there any other volumes needed in sat test ? please help. thanks in advance
!(8 votes)
- When the value of pi is not given in the question, what should we take the value as? Should we take it as 3.14, or 22/7 or something else? Please help!(5 votes)
- Pi exactly. Most calculators have a pi button, if not use 22/7(18 votes)
- At3:20Sal used a calculator, how does he know which problems he should use a calculator in?(3 votes)
- In the SAT there are two distinct sub-sections of the math section: without calculator and with calculator. Depending on the section you're doing, you'd know while doing the exam whether or not you're allowed a calculator. When Sal does the example problems he doesn't always tell us, unfortunately, but when doing questions in the SAT practice on KA you know by looking next to the "Question _ of _." There's either a calculator icon or a calculator icon with a slash across it to tell you.(17 votes)
- are these videos old? because you said they will give us the formulas and we can use calculator foe all of the questions.(8 votes)
- yup 9-10 yrs old(5 votes)
- Will the formulas be given to us?(6 votes)
- Yes, a formula sheet will always be found in the booklet(8 votes)
- How did you even get 0.8?(3 votes)
- 80 Percent means 80 per cent, per means over and cent means 100.
s0, 80 Percent= 80/100= 0.8(11 votes)
- why divide my 3?(3 votes)
- volume of cuboid= lxbxh
volume of pyramid= 1/3xlxbxh
it is divided by three because if we don't it will give us the volume of cuboid. A pyramid is 1/3 of cuboid's volume that's why we divide it by 3. hope this helps you.(10 votes)
- At2:27, he multiplied the 3 by the 4/3 only. Instead, of multiplying it by the whole expression. Isn't that wrong?(3 votes)
- how 80% is 0.8(2 votes)
- Can I tell you a secret? The percent symbol % is actually just a 1 with two 0's meaning to say divide by 100 and any number divided by 10, or 100, or 1000,etc... you just move the decimal to the left once for each zero... so that means that 20% can also be written as .2 and 37% would be .37 (and 80/100 would be 0.8!)(4 votes)
- 3:28-3:31Why did he divide should he muilpty?(3 votes)
- to make it simpler because we gonna divide by 3 anyways even if we get a product of the multiplications. so why not cancel it out to make work easier.(2 votes)
Video transcript
- [Instructor] A tea infuser
in the shape of a right rectangular pyramid is
7.9 centimeters tall and has a base three centimeters long and 1.5 centimeters wide. To make the best tea,
the infuser should be 80% filled with tea. What is the volume of
tea, in cubic centimeters, needed to fill the infuser
to 80% of its capacity. Round to the nearest tenth. All right, so this tea
infuser, it's kind of one of those fancy teabags
that hold their shape, is in the shape of a
right rectangular pyramid. So it's gonna look something like this. Let's see, its base is three centimeters by 1.5 centimeters, so it's base is, let's say that's three centimeters by 1.5 centimeters, so it
might look something like that. So that's its base. Let me draw that. Actually, I can even label it, so this is three centimeters,
this is 1.5 centimeters, and then it is 7.9 centimeters tall. So if we went from the center, and if we were to go straight up, it's 7.9 centimeters tall. So this dimension right over
here is 7.9, 7.9 centimeters, and it's a right rectangular period, so you could kind of think
of the pyramids in Egypt, although this one, this one's, this one's a little taller,
relative to its base than those, but you might have seen these fancy tea infusers. So it's gonna look something like this, and if it was transparent,
wou could be able to see this one right back here. So what we can do is, we
can first find the volume of this right rectangular
pyramid, and then they say that it should be 80% filled with tea, so we need to figure out
what 80% of its volume is, and then that's gonna tell
us what's the volume of tea needed to fill the infuser
to 80% of its capacity. Now, you might be saying, how
do I figure out the volume of a right rectangular pyramid? Well I'm about to tell you that. And there's a formula, I'm
not gonna prove it here, especially if you're
the middle of the SATs, not a lotta time for proofs,
but the formula here, in some ways, is strangely intuitive. You multiply essentially the base, the area of
the base times the height and then divide that by three. And so what's the area of the base, well it's going to be, it's going to be the length times the width, the length times the width. And then you multiply
that times the height, so it's gonna be the length times the width, times the height, and then divide it by three. So in this case it's going
to be, and just another way of thinking about it,
this right over here, the length times the
width, that's the area of this base, and then you
multiply it times the height, and then you divide by three. If you didn't divide by three,
you would get the volume of the cube, not the cube, I should say, the rectangular prism, it's not a cube, all the dimensions aren't the same. That would, that would contain this thing. But we're not concerned about the volume of the rectangular prism, we are concerned with the volume of
the right rectangular pyramid. And so this is going to be,
length, three centimeters, times width of 1.5 centimeters, times height of 7.9 centimeters, divided by, divided by three. Well, this three, three
divided by three is just one. And let's see, you have
centimeters, whoops. This is, actually, let me just change. This is centimeters right over here, divided by three. That cancels with that,
you have centimeters times centimeters times centimeters, it's going to be centimeters cubed. So your volume's going to be, let's see, it's going to be 1.5 times 7.9 centimeters cubed, or cubic centimeters. Now that's the volume of
the entire, of the entire fancy, I guess, tea infuser,
I call them fancy teabags. But we wanna know what
80% of its capacity is, because that's how much tea we need. So we wanna multiply this times 80%. So you would multiply 0.8 times 1.5 times 7.9 centimeters cubed. And let's see, 0.8 times 1.5. Let's see, that would be .8 plus .4, so this part, this is gonna be 1.2 times 7.9 centimeters cubed. We could try to approximate this. In fact, this is looking
approximately right, but we could use a calculate here, so let's just, let's
just feel good about it. So if we say 1.2 times 7.9, we get 9.48. 9.48, and if we round
to the nearest tenth, well, round to the nearest tenth. We have an eight in the hundreds place, we're gonna round up to 9.5, which is exactly that choice.