A cone-shaped plastic cup has a height of 8 inches and a radius of 3 inches If you pour water into the cup until the waters depth is 4 inches what fraction of the cup is full of water?

Answer 1

Should be 1/16 of it's volume. Using similar triangles, you can find that the radius for water is .75 inches. Then, using V=(1/3)*pi*h*r^3 for the volume of the cone and dividing the volume of water by the total volume of the cone, you should get:

Vw/Vt = (hw*rw^3)/(ht*rt^3)

where all the values with w are the water ones and all the variables with t are for the whole cone.