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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).

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

853.3

step-by-step explanation: