Q:

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

A:
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