Volume of a Rectangular Prism with Fractional Edge Lengths

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

Formula for the volume of sopd 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 sopd = l × k × w × k × h × k cubic units

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

Solution

Step 1:

Sopd of cubes with unit fraction edge lengths

Step 2:

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

= $9 imes frac{3}{4} imes 4 imes frac{3}{4} imes frac{16}{3} imes frac{3}{4}$

= 81 cu cm

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

Solution

Step 1:

Sopd of cubes with unit fraction edge lengths

Step 2:

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

= $13 imes frac{1}{3} imes 15 imes frac{1}{3} imes 15 imes frac{1}{3}$

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