Question

the volume of a cube is found by multiplying its length by its width and height. if an object has a volume of $8\\ m^3$, what is the volume in cubic centimeters? remember to multiply each side by the conversion factor.

Explanation:

Step1: Recall the conversion factor between meters and centimeters

We know that \(1\) meter \( = 100\) centimeters, so \(1\space m=100\space cm\). For volume, since volume of a cube (or any rectangular prism) is \(V = l\times w\times h\), when converting cubic meters to cubic centimeters, we need to convert each dimension (length, width, height) from meters to centimeters. So the conversion factor for volume from cubic meters to cubic centimeters is \((100\space cm / 1\space m)^3\).

Step2: Calculate the conversion factor

First, calculate \((100)^3\). We know that \(100^3=100\times100\times100 = 1000000\). So \(1\space m^3=(100\space cm)^3 = 1000000\space cm^3\).

Step3: Convert the given volume

The given volume is \(8\space m^3\). To convert this to cubic centimeters, we multiply by the conversion factor. So \(V = 8\space m^3\times\frac{1000000\space cm^3}{1\space m^3}\). The \(m^3\) units cancel out, and we have \(8\times1000000\space cm^3\).

Step4: Perform the multiplication

\(8\times1000000 = 8000000\).

Answer:

The volume in cubic centimeters is \(8000000\space cm^3\)