Answer:
5.09 cm ( to nearest hundredth).
Step-by-step explanation:
First we need to find the height of the gizmo above the plate.
This = the radius of the hemisphere + height of the cylinder.
The volume of the hemisphere = 1/2 * 4/3 * π * 0.8^3
= 1.072 cm^3.
Therefore the volume of the cylinder
= Volume of the gizmo - volume of the hemisphere
= 9.2 - 1.072
= 8.128 cm*3
Volume of the cylinder = 8.128 = π r^2 h
= π * 0.8^2 h
Height h of the cylinder = 8.128 / ( π * 0.8^2)
= 4.04 cm
So the height of the gizmo = 4.04 + 0.8
= 4.84 cm
Consider the triangle whose hypotenuse is the rod:-
sin 72 = 4.84 / x where x = length of the rod.
x = 4.84 / sin 72
= 5.09 cm (answer).
