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?

Question

Elizabeth Wood

Mathematics

23 June, 03:02

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?

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Mariyah Skinner · Answer 1

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