Y = √x and y = x³
these curve meet when x³ = √x
=> x = 0 or 1
y = √x is higher than x³ between x= 0 and x = 1.
areas under the curves / enclosed by the curves :
at any x, the radius of the circular cross section of the paraboloid is y..
Volume of an infinitesimal volume of a disc of radius y and thick ness dx
= π y² dx
the equation of the curve is y = √x or x = y²
Volume of the paraboloid :
R = 50.0 ft
A = 2 π / 3 radians = 120 deg. = 2π/3 radians
Height raised by, when the wheel turns by 90 deg. = 1 radius. = 50 ft.
as the person is at the level of the center of the wheel.
height raised by, when the wheel turns by 30 deg more = R Sin (2π/3 - π/2) = R/2 = 25 ft.
The height above the ground = 25 + 50 = 75 feet..
Angular speed = ω = angle turned / time duration = [ 2 π /3 ] / 30 sec
= π / 45 radians / sec
= 0.0698 radians / sec