![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 .](https://image.slidesharecdn.com/findingvolumeofasolidusingcross-sectionalareas-130205172342-phpapp02/85/Finding-volume-of-a-solid-using-cross-sectional-areas-2-320.jpg)
![2
Base: y 16 x , [ 4,4]
Cross sections perpendicular to the x - axis
are equilateral triangles .
4
4
-4](https://image.slidesharecdn.com/findingvolumeofasolidusingcross-sectionalareas-130205172342-phpapp02/85/Finding-volume-of-a-solid-using-cross-sectional-areas-3-320.jpg)
![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](https://image.slidesharecdn.com/findingvolumeofasolidusingcross-sectionalareas-130205172342-phpapp02/85/Finding-volume-of-a-solid-using-cross-sectional-areas-4-320.jpg)
![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](https://image.slidesharecdn.com/findingvolumeofasolidusingcross-sectionalareas-130205172342-phpapp02/85/Finding-volume-of-a-solid-using-cross-sectional-areas-5-320.jpg)
![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](https://image.slidesharecdn.com/findingvolumeofasolidusingcross-sectionalareas-130205172342-phpapp02/85/Finding-volume-of-a-solid-using-cross-sectional-areas-6-320.jpg)
Finding volume of a solid using cross sectional areas
- 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