1. Stephanie Yang G11 AP-Calculus

2. Find the volume of a solid with given
base and cross-sections.
2
Base: y 16- x , [ 4, 4 ]
Cross sections perpendicular to the x - axis
are equilateral triangles .

3. 2
Base: y 16 x , [ 4,4]
Cross sections perpendicular to the x - axis
are equilateral triangles .
4
4
-4

4. 2
Base: y 16 x , [ 4,4]
Cross sections perpendicular to the x - axis
are equilateral triangles .
( x, 16 x2 ) s ( 16 x 2 0) 2 ( x x) 2
( 16 x 2 ) 2
s
16 x 2
(x,0)
Distance formula to find the
length of a side

5. 2
Base: y 16 x , [ 4,4]
Cross sections perpendicular to the x - axis
are equilateral triangles .
Area of an equilatera l triangle
( x, 16 x 2 ) 3 2
s
4
s s 16 x 2
(x,0)
s
3 3
Area of each cross - section ( 16 x 2 ) 2 (16 x 2 )
4 4
3 2
4 3 x
4

6. 2
Base: y 16 x , [ 4,4]
Cross sections perpendicular to the x - axis
are equilateral triangles . ( x, 16 x2 )
4
4
3 2 3 3 s
V (4 3 x )dx 4 3x x (x,0)
4
4 12 4
3 3 3
4 3 (4) (4) (4 3 ( 4) ( 4) 3 )
12 12
16 3 16 3
16 3 16 3
3 3
32 3 (96 32) 3
32 3
3 3
The volume of the solid formed is
64 3
64 3 .
3
3