The length of a rectangle is 4 inches longer than its width. The area of the rectangle is 12 square inches. What are the length
and
width?
Which equation models this problem?
04.w = 12
Ow(4 + w) = 12
OW-(4 + w) = 12
OW+ (4 + w) = 12
width?
Which equation models this problem?
04.w = 12
Ow(4 + w) = 12
OW-(4 + w) = 12
OW+ (4 + w) = 12
1 answer:
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Answer:
The correct answer B) The volumes are equal.
Step-by-step explanation:
The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,
which when evaluated gives 4pi/3.
Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,
If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.