# The total area of a cylinder is 40. If height = 8, find the radius. (The formula for total area used in class is: Total area = 2πrh + 2πr²)

Friday, July 23rd, 2010

### Solution:

The total area is  40π=2πrh+2πr^2
=2πr*8 + 2πr²
=16πr + 2πr²
=16r + 2r²

If we rearrange the terms and divide the terms by 2 (in order to simplify the equation), we get:

r2 + 8r – 20 = 0

(r+10)  (r-2) = 0

r = 2  or  -10

Therefore, r = 2 (assuming that -10 is not an option!).

# In trapezoid ABCD the median MN cuts diagonals AC =D at p and q repectively, BC=12, and AD=20 Determine PQ please explain your steps. i know the median is 16 and I know the correct answer is 4, I know there is a formula but we have not proved it.

Friday, July 23rd, 2010

### Solution:

First, let’s draw the trapezoid so that we can visualize the problem. We have not drawn the trapezoid exactly to scale, but this should be accurate enough for our purposes: Now, we know that MN = 16 because the median equals the average of the top and bottom of the trapezoid We also know that the distance of Mp = 6, because it just be half the length of BC (the sides of triangle AMp are half the size of the sides of triangle ABC because the triangles are similar and we know that AM is half the length of AB since MN is the median).Similarly,the length of qN = 6.

Now it’s easy to solve for pq:

1. Mp + pq + qN = MN = 16
2. 6 + pq + 6 = 16
3. pq = 4