After painting his porch, jamil has \dfrac14 4 1 start fraction, 1, divided by, 4, end fractionof a can of paint remaining. the can has a radius of 888 cm and a height of 202020 cm. he wants to pour the remaining paint into a smaller can for storage. the smaller can has a radius of 555 cm. what does the height of the smaller can need to be to hold all of the paint?

The height of the smaller can would need to be 12.8 cm.

First find the volume of the larger can of paint.  The volume of a cylinder is given by the formula
V=πr²h

Using the dimensions of the larger can, we have
V = 3.14(8²)(20) = 4019.2

Since he has 1/4 of this can, divide the volume by 4:
4019.2/4 = 1004.8

We will use this as the volume of the smaller can.  Substituting this in along with the radius of the smaller can (using the same volume formula), we have:
1004.8 = 3.14(5²)h
1004.8 = 78.5h

Divide both sides by 78.5:
1004.8/78.5 = 78.5h/78.5
12.8 = h