1. ## cylinder

Any tips?

Let r be a positive constant. Consider the cylinder $\displaystyle x^2 + y^2 \leq r^2$, and let C be the part of the cylinder that satisfies
$\displaystyle 0 \leq z \leq y .$

a) Consider the cross section of C by the plane x = t ($\displaystyle -r \leq t \leq r .$), and express its area in terms of r,t.

b) Calculate the volume of C, and express it in terms of r.

c) Let a be the length of the arc along the base circle of C from the point (r,0,0) to the point ($\displaystyle rcos \theta, rsin \theta, 0) 0 \leq \theta \leq \pi .$
Let b be the length of the line segment from the point ($\displaystyle rcos \theta, rsin \theta, 0)$ to the point $\displaystyle (rcos \theta, rsin \theta, rsin \theta).$ . Express a and b in terms of $\displaystyle r, \theta.$ .

d) Calculate the area of the side of C with $\displaystyle x^2 + y^2 = r^2$, and express it in terms of r.

2. ## Re: cylinder

Can someone relocate to the topic calculus?

3. ## Re: cylinder

Originally Posted by provasanteriores
Can someone relocate to the topic calculus?
I presume you are in a Calc class, but the topic is Geometry so it's in the right place.

-Dan

4. ## Re: cylinder

I found the area = h²/4 ??
The answer is (r² - t²)/2

5. ## Re: cylinder

the are is (2sqrt(r²-t²).(sqrt(r²-t²)/4 = (r²-t²)/2 ?

6. ## Re: cylinder

Originally Posted by provasanteriores
Any tips?

Let r be a positive constant. Consider the cylinder $\displaystyle x^2 + y^2 \leq r^2$, and let C be the part of the cylinder that satisfies
$\displaystyle 0 \leq z \leq y .$

a) Consider the cross section of C by the plane x = t ($\displaystyle -r \leq t \leq r .$), and express its area in terms of r,t.

b) Calculate the volume of C, and express it in terms of r.

c) Let a be the length of the arc along the base circle of C from the point (r,0,0) to the point ($\displaystyle rcos \theta, rsin \theta, 0) 0 \leq \theta \leq \pi .$
Let b be the length of the line segment from the point ($\displaystyle rcos \theta, rsin \theta, 0)$ to the point $\displaystyle (rcos \theta, rsin \theta, rsin \theta).$ . Express a and b in terms of $\displaystyle r, \theta.$ .

d) Calculate the area of the side of C with $\displaystyle x^2 + y^2 = r^2$, and express it in terms of r.
Some letter c?