Standard Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas $V = l w h$ and $V = b h$ to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Computing Volume Progression 3

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Alignments to Content Standards: 6.G.A.2

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Task

A rectangular tank is $50\text{ cm}$ wide and $60\text{ cm}$ long. It can hold up to $126$ $\ell$ of water when full. If Amy fills $\frac23$ of the tank as shown, find the height of the water in centimeters. (Recall that $1$ $\ell = 1000\text{ cm}^3$.) Partially_filled_tan_0d66da946a82c1025aee5f8c0894fe8e

IM Commentary

This is the third in a series of four tasks that gradually build in complexity. The purpose of this series of tasks is to build in a natural way from accessible, concrete problems involving volume to a more abstract understanding of volume. Here, we are given the volume and are asked to find the height. In order to do this, students must know that $1$ $\ell = 1000$ $cm^3$. This fact may or may not need to be included in the problem, depending on students’ familiarity with the units.

Solution

First, find the volume of tank in cubic centimeters: $$126 \ell \times \frac{1000\text{ cm}^3}{1 \ell} =126 \times1000\text{ cm}^3 .$$ The height of tank is the volume divided by the length and the width: $$\frac{126 \times 1000}{50 \times 60} = 42\text{ cm}.$$ The height of water is $\frac23$ the height of the tank: $$ \frac23 \times 42 = 28.$$ So the height of the water is $28\text{ cm}$.

Computing Volume Progression 3

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