Cone Shaped Plastic Cup Has Height Of 8 Inches And Radius Of 3 Inches If We Pour Water Into The Cup Until The Water's Depth Is 4 Inches What Fraction Of Cup Is Full Of Water?

First we will find the volume of the whole cup (cone) and then find the volume of water in it to determine what fraction of the cup is full.

Volume of cone:
Formula:

V = 1/3 pi x r² x h

Volume of cup:

V = 1/3 x 3.14 x 3² x 8
V = 75.36 cubic inches

Volume of water:

V = 1/3 x 3.14 x 3² x 4
V = 37.68 cubic inches

Fraction of cup occupied by water:

Volume of water
Volume of cup

= 37.68/75.36

= 0.5

= 1/2

Therefore, the cup is 1/2 full of water.