2 answers:
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I've attached a plot of one such cross-section (orange) over the region in the x-y plane (blue), including the bounding curves (red). (I've set 
for this example.)
The length of each cross section (the side lying in the base) has length determined by the horizontal distance
between the y-axis 
and the curve 
. In terms of 
, this distance is 
. The height of each cross section is twice the value of , so the area of each rectangular cross section should be 
.
This means the volume would be given by the integral
The length of each cross section (the side lying in the base) has length determined by the horizontal distance
This means the volume would be given by the integral
Answer:
<h3>b) 850.1 centimeters.</h3>Step-by-step explanation:
To find the area of this figure, we must first find the areas of the shapes that compose this figure.
This figure is made up of a rectangle and a semicircle.
Remember: To find the area of a semicircle, multiply the radius by itself twice, then multiply the product pi, lastly divide the product by 2.
<u>3.14 will be used for pi!</u>
To find the area of a rectangle, multiply the length by the width. The product is the area of the rectangle.
Now, let's solve.
The diameter of the semicircle is 32 centimeters.
To find the radius of a semicircle, divide the diameter by 2.
The radius of the semicircle is 16 centimeters.
Now that we have the radius, we can find the area of the semicircle.
The area of the semicircle is 401.92 centimeters.
Furthermore, we find the area of the rectangle.
The area of the circle is 448 centimeters.
Next, we add the areas of both shapes to find the area of this figure.
The final step is to round 849.92 to the nearest tenth.
Even though 849.92 to rounded to the nearest tenth is 849.9, there is no answer choice for this. The closest one to this answer is choice 'b.'
I, therefore, believe the area of this figure is 850.1 centimeters.