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?

Accepted Solution

The height must be 12.8.

We first find the volume of paint in the larger can.  The formula for the volume of a cylinder is V=πr²h.  Using the radius and height of the large can, we have

V=3.14(8²)(20) = 4019.2

Since he has 1/4 of the can left, he has 4019.2/4 = 1004.8 cm³ of paint.

Using this volume and the dimensions of the smaller can, we work backward to find the height of the paint in the can:

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