Problem

Volume and Surface Area The radius of a spherical…

09:07

Problem 35 Hard Difficulty

Volume and Surface Area The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03 inch.
(a) Use differentials to approximate the possible propagated error in computing the volume of the
cube.
(b) Use differentials to approximate the possible propagated error in computing the surface area of the cube.
(c) Approximate the percent errors in parts (a) and (b).

Answer

(a) $\pm 20.25$ cubic inches (b) $\pm 5.4$ square inches

Related Courses

Calculus 1 / AB

Calculus of a Single Variable

Chapter 3

Applications of Differentiation

Section 9

Differentials

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Video Transcript

in question 35. Um, have a cube. This is the actually the only drawing, but I can render three dimensions on that. Mmm. You. So our error is reported to be for my next really hundreds. Great. So now we're going to part end, estimate the volume. You if I get my 15 right away. Me that later. Q 3370. I'm gonna take the driven. Be with records. Yes. Meet three x were here in the you re X square B. It's well, I'll be equals three times 15 square. I'm just going in the edge of my Q times to the X, which is plus minus +03 and money 25 r b. I'm gonna do the same thing, but with surface area So surface area is the area of each of the size of the queue. My surface area it is One side of the cube is X square and I have six side client, six eggs. Weird. You were Yes, his things. Talyn's 15 where Inches square. No D s routine. X people from X therefore being s equals 12 x The ex Yes, 12 times. 15 times last year, minus three own. That equals, Let's remind us Glad. Quite poor. R c. We're doing the error. I'm using the formula. Do you know why? Over why. And this is why I figured out why so part? Ay, I have my b y money. Quite 25. And here's my 33 75. That's my well, if you Mmm. Which is, like 006 Move the desk more multiplied by 100 and you get night. 6% relative. They're presenting her. So for part, be the same thing. I would have, uh, 5.4. Blinded by ally 13. 50. We're over percent.

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