Download Volume of objects with known cross sections:

Volume of objects with known cross sections
AP Calculus
Name:
Area formulas you need to know:
1
1) semi-circle =  (radius ) 2
2
2) rectangle of height H = (base)(height)
3) square = (base)2
4) right isosceles triangle
h2
 if the hypotenuse (h) is the distance between the curves the area of the triangle =
4
L2
 if one of the legs (L) is the distance between the curves, the area of the triangle =
2
1) Suppose the space defined by the intersection between the functions
f(x) = x2 – 1 and g(x) = x + 1 is the base of a solid that is formed by building up with the following
shapes perpendicular to the x-axis. Set up the integral expression that would determine that shape’s
volume:
a) squares
b) rectangles of height 10
c) semi-circles
1) continued:
d) right isosceles triangles, with a leg on the base
e) right isosceles triangles, with a hypotenuse on the base
2) Suppose the space defined by the intersection between the equations y = x, y = 6  x , and y = 0 is
the bottom of a solid that is formed by building up with cross sections that are perpendicular to the y-axis
with the following shapes. Set up the integral expression that would find its volume
a) semi-circles:
b) rectangles that are twice as tall as they are wide
http://mathdemos.org/mathdemos/sectionmethod/sqrcross75slab.gif