Multiply using napier's rods 3x4565

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).