Question

Julie wants to transfer the water from the rectangular container pictured below to a cylindrical bucket. Will all the water fit into the new bucket?

Answer 1

Rectangular Container

V = l × w × h

V = 13 in. × 12 in. × 14 in.

V = 2,184 cu. in.

Cylindrical Bucket

V = πr²h

V = 3.14 × (7 in.)² × 14 in.

V = 3.14 × 49 sq. in. × 14 in.

V = 2,154.04 cu. in.

2,184 cu. in. > 2,154.04 cu. in.

rectangular cylindrical cylindrical bucket

Answer: The volume of the bucket is smaller than the volume of the cylindrical container. The water will not all fit into the bucket.

Answer 2

no

Explanation:

The heights of the two containers are the same, so we can compare their volumes by comparing their base areas.

Cuboid

The base area is given by ...

A = LW

A = (13 in)(12 in) = 156 in²

Cylinder

The base area is that of a circle of radius 7 inches:

A = πr²

A = π(7 in)² = 49π in² ≈ 153.9 in²

The area of the cuboid is greater, so its volume is greater that that of the cylinder. Not all of the water will fit into the bucket.

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Additional comment

For any shape having a uniform cross section, the volume is given by the formula ...

V = Bh

where B is the area of the cross section, and h is the height perpendicular to that cross section.