# Thread: Volume is smaller than area of base. Why? I thought this wasn't possible.

1. ## Volume is smaller than area of base. Why? I thought this wasn't possible

Let f and g be the functions given by f(x) = 1+sin(2x) and g(x) = eˆx/2. Let R be the shaded region in the first quadrant enclosed by the graphs of f and g as shown in the figure above.

a. Find the area of R.

b. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from y = f(x) to y = g(x). Find the volume of this solid.

I am not asking anyone to answer these two questions; I have solved them and I got the correct answers, but I don't understand why my answers are correct. The answer to part a is BIGGER than the answer to part b. How can this be true? The area of the base can't be bigger than the volume of the solid??

2. ## Re: Volume is smaller than area of base. Why? I thought this wasn't possible

Originally Posted by nicksbyman
Let f and g be the functions given by f(x) = 1+sin(2x) and g(x) = eˆx/2. Let R be the shaded region in the first quadrant enclosed by the graphs of f and g as shown in the figure above.

a. Find the area of R.

b. The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles with diameters extending from y = f(x) to y = g(x). Find the volume of this solid.

I am not asking anyone to answer these two questions; I have solved them and I got the correct answers, but I don't understand why my answers are correct. The answer to part a is BIGGER than the answer to part b. How can this be true? The area of the base can't be bigger than the volume of the solid??

Enclosed in what figure?

3. ## Re: Volume is smaller than area of base. Why? I thought this wasn't possible

Originally Posted by Prove It
Enclosed in what figure?
Sorry I don't know how to post the figure. I think that you don't need the figure to answer the question though.

4. ## Re: Volume is smaller than area of base. Why? I thought this wasn't possible

The statement "area is bigger than volume" is nonsense, since you are comparing things with different dimensions.

Is 1 foot the same as 1 inch (or 1 liter) because they both have the same number?

A sphere with radius 1 unit will have surface area of 4pi units^2, and a volume of (4/3)pi units^3...

5. ## Re: Volume is smaller than area of base. Why? I thought this wasn't possible

Perhaps you are thinking that "volume= base times height". Don't forget that the height can be less than 1.

### smaller then area./

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