Question

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?

Answer 1

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

Answer 2

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

The volume of a cylinder is given as :

V = πr²h

Volume of larger cylinder = π × 8² × 20 = 4021.24 cm³

The Fraction of paint remaining = 1/4

Hence, volume of paint left = 1/4 × 4021.24 = 1005.31 cm³

The smaller Can thus would hold a volume of 1005.31 ;

Using the formula, we find find the value of height, h;

V = πr²h

1005.31 = π × 5² × h

1005.31 = 78.539816h

h = 1005.31 / 78.539816

h = 12.8 cm

Therefore, the height of the smaller can would have to be 12.8 cm

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