Question

An ice cream company sells their product in a cylindrical

container that is 16 cm tall and has a diameter of 14 cm.

They are considering switching to a new container that is a

rectangular prism whose base is 20 × 13 cm.

The company wants the new container to have the same

volume as the old container.

How tall should the new container be?

Answer 1

9.5 centimeters tall

Explanation:

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Answer 2

9.5 cm

Explanation:

You want the height of a 20 cm by 13 cm cuboid container that has the same volume as a cylindrical container 14 cm in diameter and 16 cm tall.

Volume

The volume of the cylinder is ...

V = (π/4)d²h

V = (π/4)(14 cm)²(16 cm) ≈ 2463 cm³

The volume of the rectangular container is ...

V = LWH

2463 cm³ = (20 cm)(13 cm)H . . . . . . . . . . . use the known values

H = (2463 cm³)/(20·13 cm²) ≈ 9.473 cm . . . . . solve for height

The new container should be about 9.5 cm tall.

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