Question

the volume of this cube is 2,146.689 cubic feet. what is the value of v? v = feet

Explanation:

Step1: Recall the volume formula for a cube

The volume \( V \) of a cube with side length \( v \) is \( V = v^{3} \). Given \( V=2146.689 \), we have the equation \( v^{3}=2146.689 \).

Step2: Solve for \( v \)

To find \( v \), take the cube - root of both sides. So \( v=\sqrt[3]{2146.689} \).
Using a calculator, \( \sqrt[3]{2146.689}=12.9 \) since \( 12.9\times12.9\times12.9=(13 - 0.1)\times(13 - 0.1)\times(13 - 0.1)=(169-2.6 + 0.01)\times(13 - 0.1)=(166.41)\times(13 - 0.1)=2163.33-16.641 = 2146.689\).

Answer:

\(12.9\)