* Site-Outage Notice: Our engineering elves will be tweaking the Shmoop site from Monday, December 22 10:00 PM PST to Tuesday, December 23 5:00 AM PST. The site will be unavailable during this time.
Dismiss
© 2014 Shmoop University, Inc. All rights reserved.
Area, Volume, and Arc Length

Area, Volume, and Arc Length

Area, Volume, and Arc Length: Making Mercury: Free Fish Sticks Quiz

Think you’ve got your head wrapped around Area, Volume, and Arc Length? Put your knowledge to the test. Good luck — the Stickman is counting on you!
Q. Let R be the finite region bounded by the graphs y = x2, y = 6 – x, and x = 4. Which picture shows R as the shaded region?



Q. Which of the following integrals give the area of the shaded region?

(I) 

(II) 

(III)  

(IV)



(I) and (III)
(I) and (IV)
(II) and (III)
(II) and (IV)
Q. Let R be the region bounded by the graphs of y = x and . Which of the following integrals give the area of R?

(I) 

(II) 

(III) 

(IV) 



(I) and (III)
(I) and (IV)
(II) and (III)
(II) and (IV)
Q. Let R be the region graphed below.

Which of the following integral expressions give the area of R?

(I)

(II) 

(III)  



(III) only
(I) and (II)
(I) and (III)
(II) and (III)
Q. Which of the following integrals gives the area of a right triangle whose non-hypotenuse sides have lengths 7 and 9?


Q. Which of the following is the area of the unit circle?


Q. A square has a diagonal of length 10. Which of the following expressions does NOT give the area of the square?


100
Q. Below is a graph of the polar function r = f(θ).

The area of the shaded region is



Q. What is the area of one petal of the graph of the polar function r = 1 + cos(3θ)?


Q. What is the area of the shaded region?



Advertisement
Noodle's College Search
Advertisement
Advertisement
Advertisement