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
Answer:
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
solved
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