Posted by Rebekah on Wednesday, September 19, 2012 at 6:53am.
Water is poured into a container in the sape of a right circlar cone with raiud 4t an heigh 16 feet. Express the volue (V) of the water in the cone as a funtio of the heigh (h) of the water.
- pre calc - Damon, Wednesday, September 19, 2012 at 7:48am
I can not read your radius so call it R.
I assume the point of the one is down.
the radius of the water surface at height h is r = (16/R)h
the area of that water surface is pi r^2
The volume of a horizontal slice dh is
pi r^2 dh
pi (16/R)^2 h^2 dh
so integrating the volume at height h is
V(h) = pi (16/R)^2 h^3 /3
if for example R were 4 feet then
V(h) = pi (16/3) h^3
- pre calc - Steve, Wednesday, September 19, 2012 at 11:10am
or, just using similar cones, at height h, the surface of the water has a radius which can be found by
R/16 = r/h
r = hR/16
v = 1/3 pi r^2 * h
= pi/3 (hR/16)^2 * h
= pi/3 * R^2/256 * h
Hmmm. Better check both our maths - we disagree.
- pre calc - Reiny, Wednesday, September 19, 2012 at 11:45am
or , assuming you are saying the radius of the cone is 4 ft,
let the height of water be h
and the radius of the water level be r
r/h = 4/16 = 1/4
r = h/4
V = (1/3)πr^2 h
Answer This Question
More Related Questions
- calculus - A hollow cone has height 5 feet and base diameter 4 feet. The vertex...
- Geometry - A cone and cylinder both have a radius of 3 inches and a height of 6 ...
- math - Water is poured into a right circular cone with a height of 10 cm and ...
- Calculus - A container in the form of a right circular cone (vertex down) has a...
- Math - A tank in the shape of a cone has a diameter of 8 feet and a height of 10...
- math - A cylinder container of radius 15 cm has some water in it. When a solid ...
- Calculus - A vessel is in the shape of an inverted cone. The radius of the top ...
- math - a vessel comtaining water has the shape of an inverted circular cone of ...
- Math - the formula for the volume of a cone is v=1/3pir^2h. The volume cone x is...
- Calculus - A water tank is shaped like an inverted right circular cone with a ...