Question

a rectangular prism is 21 ft tall and has a square base with a width of 8 ft. what is \\( \frac { 3 } { 4 } \\) of the volume of the figure in cubic ft?

Explanation:

Step1: Calculate the volume of the rectangular prism

The formula for the volume \(V\) of a rectangular prism is \(V = l\times w\times h\). Since the base is square, \(l = w=8\) ft and \(h = 21\) ft. So \(V=8\times8\times21\).
First, \(8\times8 = 64\). Then \(64\times21=(60 + 4)\times21=60\times21+4\times21=1260+84 = 1344\) cubic ft.

Step2: Find \(\frac{3}{4}\) of the volume

Multiply the volume by \(\frac{3}{4}\). So \(\frac{3}{4}\times1344\).
Since \(1344\div4 = 336\), then \(336\times3=1008\) cubic ft.

Answer:

1008