Which function's graph has x-intercepts at x = - 2 and x = 4 , and a vertex at point (1, - 18) ?
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.
The approximate volume of each slice will be 63.5 inch². The total cake is divided into the four cylindrical slice.
<h3>What is volume?</h3>
It is defined as a three-dimensional space enclosed by an object or thing.
The volume of the slice is;
If the grandma cut four pieces, is the approximate volume of each slice that Hattie's grandma cut will be;
The approximate volume of each slice will be;
Hence, the approximate volume of each slice will be 63.5 inch².
Learn more about the volume here:
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