Lesson 12.3 Day 2 started.notebook
12.3 Day 2 Quadric Surfaces
March 12, 2012
Lesson 12.3 Day 2 started.notebook
March 12, 2012
Submarine Problem : The submarine pressure hull can be built in the shape of a frustum of a cone. A frustum of a cone is a cone with its vertex cut off. The larger base of the frustum is the base of the half ellipsoid. The smaller base of the frustum touches the half ellipsoid at the sample point (x,y). 225 x 2 + 900 y 2 = 202,500
.
(x,y)
Lesson 12.3 Day 2 started.notebook
March 12, 2012
A. Prove the volume of the frustum of a cone is V = 1/3 π h ( R 2 +Rr + r 2) where h is the altitude of the frustum ( between the two circular bases)
and R and r are the radii of the two bases.
.
(x,y)
Lesson 12.3 Day 2 started.notebook
March 12, 2012
B. Find the maximum volume the frustum can have.
12.3 Day 3 Continued ­ Maximizing Area/Volume using Conic Sections
Lesson 12.3 Day 2 started.notebook
Roads are often designed with parabolic surfaces to allow rain to drain off. A particular road that is 32 ft. wide is 0.4 foot higher in the center than it is on the sides.
A. Find an equation of the parabola that models the
road surface.
B. How far from the center of the road is the road
surface 0.1 foot lower than in the middle ?
Find the points on the ellipse 4 x 2 + y 2 = 4
that are the farthest away from the point ( 1 , 0 ).
March 12, 2012
Lesson 12.3 Day 2 started.notebook
Find the dimensions of the rectangle of largest area that has its base on the x­axis and its other two vertices above the x­axis and lying on the parabola y = 8 ­ x 2.
March 12, 2012