solving volumes using cross sectional areas
TRANSCRIPT
SOLVING VOLUMES US-ING CROSS SECTIONAL AREAS
AP Calculus AB/ Christy Sohn (11)
Solving Volume of a Cross-Sectional Solid
x
yxxy 2
2
1 2
•Base:
•Cross Sectional Shapes: • Triangles perpendicular to the
x-axis.•Interval: [0,4]
xxy 22
1 2
•Triangle Base: Triangle Height = 2:• Triangle Base= (2*(Triangle
Height))/
•Area of the Whole Triangle:
•Function for Solving the Volume of the Solid:
33
)4
3)(2*(
2
1Base
dxxx 224
0
)22
1(
3
3
Solutions
x
yxxy 2
2
1 2 dxxx
dxAreaVolume
224
0
4
0
)22
1(
3
3
)(
])424
1([(
3
3 4
0
2
54 dxxxx
)27
4
20
1(
3
34
0
22
75 xxx
)])0(2)0(7
4)0(
20
1())4(2)4(
7
4)4(
20
1[(
3
3 22
7522
75
)327
512
5
256(
3
3 )
35
5472(
3
3
26.902646.9035
31824