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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

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