I need your help ASAP!!! grade 11 applied math question.

Question

A pet store designs fish tanks that are in the shape of a rectangular prism. The small tank has a capacity of 1920 cu in. The scale factor that relates the dimensions of the small tank to the dimensions of the medium tank are 1.25. The scale factor that relates the dimensions of the medium tank to the dimensions of the large tank are 1.2.

Glass costs the store $12 to put in the small tank.

Find the capacity of the medium and large tanks and find the cost of the glass for the medium and large tanks.

please show all work.

Answer 1

It seems too late to help, but hopefully, you can use this for future reference.

A scale factor is how much we are looking to increase the size of a shape. So, if we had a scale factor of 2, we would want the new shape to be two times larger. In this case, the medium tank would be 1.25 times larger than the small tank and the large tank would be 1.2 times bigger than the medium tank. But, don't just start multiplying the volume by 1.25. We have to take into account that we are working with volume/cu in instead of a flat shape. When working with volume, we have to first take the scale factor to the third power. That's because we have three dimensions and each dimension has to be multiplied by the scale factor.

The work for this would look like:

n³ x the volume= the volume of the medium tank

1.25³ x 1920cu in= 3750cu in

m³ x volume of medium tank= volume of large tank

1.2³ x 3750cu in= 6480cu in

We now know that the volume of the medium tank is 3750cu in and the volume of the large tank is 6480cu in.

Next, we have to figure out the price. To find the prices for the tanks, we would need to multiply the price by the cubed scale factors as well. Again, the prices for the glass are based on the dimensions of the glass needed. We have three dimensions (length, width, and height). To accommodate for those three dimensions, we would need to use cubed square factors again in order to get an accurate price.

The work for this would look like:

n³ x 12= price of medium tank

1.25³ x 12= $23.44 (rounded)

m³ x 23.44= price of large tank

1.2³ x 23.44= $40.50 (rounded)

The small tank is 1920cu in and costs $12.

The medium tank is 3750cu in and costs $23.44.

The large tank is 6480cu in and costs $40.50.