# Volume of a Rectangular Prism with Fractional Edge Lengths

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In this lesson, we find the volume of rectangular prisms with fractional edge lengths.

Formula for the volume of solid made of cubes with unit fractional edge lengths

l = number of cubes with unit fractional edge length along the length

w = number of cubes with unit fractional edge length along the width

h = number of cubes with unit fractional edge length along the height

k = unit fractional edge length

Volume of solid = l × k × w × k × h × k cubic units

Find the volume of following solid of cubes with unit fraction edge lengths. Each prisms unit is measured in cm (not to scale) ### Solution

Step 1:

Solid of cubes with unit fraction edge lengths Step 2:

Volume V = l w h = $6 \frac{3}{4} \times 3 \times 4$

= $9 \times \frac{3}{4} \times 4 \times \frac{3}{4} \times \frac{16}{3} \times \frac{3}{4}$

= 81 cu cm

Find the volume of following solid of cubes with unit fraction edge lengths. Each prisms unit is measured in cm (not to scale) ### Solution

Step 1:

Solid of cubes with unit fraction edge lengths Step 2:

Volume V = l w h = $4 \frac{1}{3} \times 5 \times 5$

= $13 \times \frac{1}{3} \times 15 \times \frac{1}{3} \times 15 \times \frac{1}{3}$

= $108 \frac{1}{3}$ cu cm