Mth 163

There is a question in the homework which asks, What is the volRatio for a pair of cubes with edges 12.7 and 2.3 (the ratio is [second volume]/[first volume]?

Right. The volume of the first cube would be 12.7 * 12.7 * 12.7 = 2000 or so, and the volume of the second would be 2.3 * 2.3 * 2.3, or about 11 or 12. The ratio would be [second volume] / [ first volume].

Then it asks, What is the edge ratio^3? Does this mean the second volume divided by the first volume then raise that answer to the power of three?

This means to find the edge ratio, and cube it. The edge ratio is 12.7 / 2.3. What is this number, and what is its cube?

I ask this because an earlier question led me to believe that we were to cube the volumes first before dividing, or were we doing something different by cubing the numbers first?

Right. The volume of the first cube would be 12.7 * 12.7 * 12.7 = 2000 or so, and the volume of the second would be 2.3 * 2.3 * 2.3, or about 11 or 12. The ratio would be [second volume] / [ first volume].

This means to find the edge ratio, and cube it. The edge ratio is 12.7 / 2.3. What is this number, and what is its cube?

You cube the edge length to get the volume; we haven't encountered a case where you cube the volume.