Set A Set B
. .
...
....
0 2 4 6 8
2 4 6
810
O A. The typical value and the spread are both greater in set B.
B. The typical value and the spread are both greater in set A.
O C. The typical value is greater in set B. The spread is greater in set A.
D. The typical value is greater in set A. The spread is greater in set B.

I believe C is the correct answer, please let me know if it is wrong

V =  

Explanation:

In the given system of coordinates OXY, the region R₃ is bounded by two functions:

y₁ =  (green line)

y₂ = 2x  (blu line)

in the intervals:

0 ≤ x ≤ 1

0 ≤ y ≤ 2

We need to find the volume of this region rotated about the line AB, which is x = 1. In order to do so, we need to change system of coordinates, such as the rotation is about the y-axis, therefore we need to perform a translation:

After the translation R₃ will be bounded by:

y₁ =

y₂ = 2x + 2

in the intervals:

-1 ≤ x ≤ 0

0 ≤ y ≤ 2

At this point, we can use the washer method (see picture attached). The general formula is:

A = π(R² - r²)

where:

A = area

R = outer radius of a washer

r = inner radius of a washer

Since the radii are x-values which vary with the height, represented by the y-values, we need to write the inverse functions:

[Note: I used the curves on the left side of the graph, but you could find the ones representing the right side of the graph and use those]

Now, we can find the function for the area of each washer:

Therefore the volume of the region R₃ will be: