Using volume for missing side length (mixed numbers)
About this video
A rectangular box has volume 7 1/2 cubic inches, width 3 inches and height 2 inches. The video writes 2 x 3 x l = 15/2, so 6 x l = 15/2, and divides: l = 15/2 x 1/6 = 15/12 = 5/4, so the length is 1 1/4 inches.
You'll be able to
- use volume = width x height x length to find a missing side length.
- change a mixed number into an improper fraction.
- divide a fraction by a whole number by multiplying by its reciprocal and simplify the result.
Key words
- volume
- The space inside a box, found by multiplying width, height and length.
- improper fraction
- A fraction whose top number is bigger than its bottom number, like 15/2.
- cubic inches
- The unit for volume when lengths are measured in inches.
- simplify
- Divide the numerator and denominator by the same number to write a fraction in smaller numbers.
Transcript
- [Instructor] We're told a rectangular storage box has a volume of 7 1/2 cubic inches. The box is three inches wide and two inches tall. What is the length of the storage box? So pause this video. Have a go at this before we do this together. Okay, so let's just draw this box out.
It's not being drawn accurately to scale, but at least we can visualize it. So we know that it is three inches wide. We'll assume everything is in inches 'cause that's the units that we see here, three inches wide, two inches tall. And we need to figure out the length of the box.
So this is the length right over here. Maybe we call that l for length. So we wanna know what that is. Now luckily we know that the volume is 7 1/2 cubic inches. So what we know is if we take the width times the height times the length, then we're going to get 7 1/2.
So let's write that down. So if I were to take two inches times three inches times l inches, I am going to get 7 1/2. And since I think I'm going to have to do a little bit of multiplying and dividing, let me write that as what's sometimes called an improper fraction.
So let's see, if I have... 7 1/2 is the same thing as... Seven is 14 halves, plus 1/2 is 15 halves. Is equal to 15 halves or 15/2 cubic inches, cubic inches. Or another way to think about it, I won't keep writing the units. I think you get the idea there. If we take two times three times l, we're gonna get six times l.
Six times l is equal to... Let me just, I'll put the times there just to... We could also just write six l, but let me just write this way, is equal to 15/2. Or another way to think about it is l is equal to 15/2 divided by six, or that's the same thing as 15/2 times 1/6.
I could write times that way. I could also write it that way if I want. And this is going to be equal to 15/12. Just multiply the numerator, multiply the denominator. And I can write this a little bit simpler if I want. Both the numerator and the denominator is divisible by three.
So if I divide them both by three, I'm going to get 5/4. So the length here is 5/4 of an inch, or that's the same thing as 1 1/4 inches. And we are done.
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