Lesson 5 - Volume of a Right Circular Cylinder #6

[One speaker]

[The word problem to be solved is displayed on the screen as the video begins.]

Narrator: A triple A battery is a right circular cylinder with a radius of 5.25 millimeters and a height of 44.5 millimeters. Find the volume of the battery. Round to the nearest tenth. [the outline of a battery appears on the right side of the screen] So here’s our battery, and let’s visualize what’s going on here. We know that we have a radius, so—a radius of—let’s get that to show up a little bit better—’kay, so our radius comes out and that is 5.25 millimeters [draws a purple dot in the center of the top of the battery and then draws a line from the center to the right edge to show the radius, after which “5.25 millimeters”]. ‘Kay, and then our height on the side here [draws a purple line down the right side of the battery] is 44.5 millimeters [writes “44.5 millimeters” to the right of the battery]. And it’s asking us to find the volume [circles the word ‘volume’ in purple] of the battery.

So we know that our volume is equal to [writes “V =” on the left side of the screen] the area of the circle, so pi R squared times the height [writes “” to the right of the equals sign]. So we have pi R squared H [adds an ‘h’ after “”]. And now we can plug in what we know. We know that our radius is 5.25 millimeters [writes “r = 5.25mm” underneath the equation just written] and our height is 44.5 millimeters [writes “h = 44.5 millimeters” underneath the radius]. So let’s plug those into our equation here—to our formula.

So we have pi times the radius squared times our height [writes “= ” ] And now we can plug this into the calculator [pulls up the calculator. So we have 5.25 [types “5.25” into the calculator]—that was our radius—we have that squared [hits the ‘’ button], and that gives us 27.5625. Let’s write that here. So we have 27.5625 millimeters squared [writes “= (27.5625” underneath the equation just written]. We’ve got—don’t forget our pi [places a  symbol to the left of the parentheses]. That is times 44.5 millimeters [writes “(44.5mm)” to the right of the first parentheses]. So let’s multiply that by 44.5 [calculator appears again]. So times 44.5 equals [types “x 44.5 =” and “1,226.53125” appears]—that gives us one thousand two hundred twenty-six point five and some numbers (1,226.53125), so let’s write that down. We have one thousand two hundred and twenty-six point five (1,226.5) [writes “= 1,226.5” at the bottom of the screen], and I’m going to round on here, but in my calculator I’m going to leave it how it was, and then multiply by pi.

‘Kay, so we have that times pi [places a ‘’ symbol next to ‘1,226.5’]. We’ve got our millimeters squared times millimeters, which gives us millimeters cubed [writes ‘’ to the right of the symbol]. And so, we could leave our answer like this, or we could go back to our calculator and multiply that by pi. [pulls the calculator back up] So times pi equals [types “x ”], and we get three thousand eight hundred fifty-three point two six (3,853.26)—and let’s see what we needed to round to. Round to the nearest tenth—so we had three thousand eight hundred fifty-three point three (3,853.3). So let’s write that. We have equals three thousand eight hundred fifty-three [writes “= 3,853” at the bottom of the screen] rounded to the nearest tenth—we have point three [adds “.3” to the right of ‘3,853’], and we have millimeters cubed [adds ‘’ at the end of the number].

So the volume of our battery would be three thousand eight hundred fifty-three point three millimeters cubed [3,853.3].

[End of video.]