Need clarification on scaling

Question

Question is: "A given rectangular prism holds 32 liters of water. If you scale the dimensions of the figure by a factor of 10, the volume of the new rectangular prism is ____ liters."

is the new volume 100 times more than the original given prism?

Do I have to find dimensions first?

Thank you!

Answer 1

Emily,

Actually the volume will be 1000 times more than the original given prism.

Here's how to figure this out: We know that the volume of the rectangular prism is 32 liters. Volume of a rectangular prism is found by multiplying length, width and height. So these 3 measurements times each other is equal to 32. These measurements could be anything, but let's just assume that the length and width are both 2 and the height is 8.

2 * 2 * 8 = 32, so this is a good assumption to use. Now let's say we multiply all these factors by 10! We would have 20, 20 and 80.

20 * 20 * 80 = 32,000 (liters)!

So, we have increased the volume of the prism by a factor of 1000.

Hope this helps. :)