Triangles with height 
and base 
, with 
have area 
.
Such cross sections with the base of the triangle in the disk 
(a disk with radius 5) have base with length
i.e. the vertical (in the 
plane) distance between the top and bottom curves describing the circle 
.
So when 
, the cross section at that point has base
so that the area of the cross section would be 6^2/2 = 18.
In case it's relevant, the entire solid would have volume given by the integral
Answer:
the teacher bought 100 balloons, and 95 of them were left for the party.
Step-by-step explanation:
red balloons is given, 40.
first you find the green balloons.
<em>the number of green balloons is 3/5 the number of red balloons.</em>
3/5 * 40 = 24
so there are 24 green balloons.
next is yellow balloons.
<em>the number of green balloons is 2/3 the number of yellow balloons.</em>
24 = 2/3 * x
24 ÷ 2/3 = x
24 ÷ 2/3 = 36
there are 36 yellow balloons.
find the total balloons:
40 + 24 + 36 = 100
the teacher bought 100 balloons.
1/20 of the red balloons popped.
1/20 * 40 = 2
2 of the red balloons popped
1/12 of the green balloons popped
1/12 * 24 = 2
2 of the green balloons popped.
1/36 of the yellow balloons popped
1/36 * 36 = 1
1 yellow balloon popped
2 + 2 + 1 = 5
100 - 5 = 95
there were 95 balloons left for the party.
Is there a picture with it?
