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# Area, Volume, and Arc Length

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

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Area, Volume, and Arc Length**Q. Let

*R*be the finite region bounded by the graphs*y*=*x*^{2},*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?

2π

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?