Saturn WY15
Member
- Joined
- May 21, 2010
- Messages
- 129
- Gender
- Male
- HSC
- 2012
The base of a solid is the region by the graphs of f(x)=x^2 and g(x) = 8 - x^2. Find the volume of solid if all the cross sections perpendicular to the x- axis are squares.
-
Looking for HSC notes and resources? Check out our Notes & Resources page
Volumes q (1 Viewer)
- Thread starter Saturn WY15
- Start date
Carrotsticks
Retired
- Joined
- Jun 29, 2009
- Messages
- 9,494
- Gender
- Undisclosed
- HSC
- N/A
Length of 'base' of square:
 = 2x^2-8 = 2(x^2-4))
So area of square is l^2, which is:
^2 = 4(x^4 - 8x + 16) )
Thickness of slice is just delta x.
Volume of one slice is:
 \delta x )
To find volume of solid, we integrate this expression (equivalent of taking the sum of infinite slices as they get infinitely thin).
The limits of integration will be the points of intersection between the two curves.
 dx)
And you can calculate the rest yourself.
So area of square is l^2, which is:
Thickness of slice is just delta x.
Volume of one slice is:
To find volume of solid, we integrate this expression (equivalent of taking the sum of infinite slices as they get infinitely thin).
The limits of integration will be the points of intersection between the two curves.
And you can calculate the rest yourself.