Truncated Right Cylinder: Find vol, given angle, shortest & longest elements

[Robertoxxx]

Hello guys, i need a bit of guidance with this problem;

In a truncated right cylinder, the top plane makes an angle of 45deg horizontal. and the shortest and longest elements are 27 and 5 units. Find the Volume.

Here's what a did so far, to find the diameter, i took out the triangle that can be formed from the top plane, with 27 and 5 as the longest/shortest units, i subtracted 27 and 5 to get the opposite side of the triangle which is 22 units.

Now that i have the angle formed in the triangle which is 45deg and 22 as the opposite side, i used the formula;

diameter = 22 / tan45, which gave me the value of 22, i then divided by 2 to get the radius which is 11.

then used the formula v=(pi)(11)^2 (27+5)/2 = 1936pi

But my professor told me that my answer was wrong, any help will be appreciated.

 

[stapel]

In a truncated right cylinder, the top plane makes an angle of 45deg horizontal. and the shortest and longest elements are 27 and 5 units. Find the Volume.

Here's what a did so far, to find the diameter, i took out the triangle that can be formed from the top plane, with 27 and 5 as the longest/shortest units, i subtracted 27 and 5 to get the opposite side of the triangle which is 22 units.

Now that i have the angle formed in the triangle which is 45deg and 22 as the opposite side, i used the formula;

diameter = 22 / tan45, which gave me the value of 22, i then divided by 2 to get the radius which is 11.

then used the formula v=(pi)(11)^2 (27+5)/2 = 1936pi

What does this formula represent? I know that the volume V of a right circular cylinder with height h and radius r is given by V = (pi)(r^2)(h). I see that you have (pi) and (r^2), but what is the meaning of "(27+5)/2"? How does this relate? What was your reasoning for this?

Instead, I would find the volume of the 5-unit tall portion, using the regular formula. Then I'd note that the 45-degree-angle bit is essentially another 22-unit tall cylinder, cut exactly in half. So what would this volume be? Then I'd add the two.