Are you taking CLEP classes? Try clep.ai
| preferred AP College board partner for AP classes
AP Calculus BC/Unit 8: Applications of Integration
Start Practice TestPractice Test
About Exam
hard

Comparing Volumes of Revolution

Mark
< Prev
Next >

Consider the region under y=xy=\sqrt{x} from x = a to 9. Rotating this region about the x-axis yields a volume given by

V(a)=π(81−(a+1)32)V(a)=\pi\left(\frac{81-(a+1)^3}{2}\right)

(for a proper antiderivative, note that here the effective volume is proportional to 81−a22\frac{81-a^2}{2}, and using the given data, assume the computed volumes for a = 1, 2, 3, and 4 are approximately 40π, 38.5π, 36π, and 32.5π respectively). Rank the intervals [0,1], [0,2], [0,3], [0,4] in order of increasing volume when the lower limit a is varied (interpret [0,a] as indicating the region starting at x=a to x=9).

A

[4,9], [3,9], [2,9], [1,9]

B

[4,9], [2,9], [3,9], [1,9]

C

[3,9], [4,9], [2,9], [1,9]

D

[1,9], [2,9], [3,9], [4,9]

Hint
Did You Know?
Explain Why
Explain All Answers
Check Answer
Show Correct Answer
Report Question

Question Leaderboard

Not enough data yet to show leaderboard.

AI Tutor

How can I help?

APFIVE © 2020.
Email: apfive@apfive.org|Privacy Policy|