Question

20 points!

Annie Mae collects snow globes that come in cube-shaped boxes as shown.


Question options:

The volume increases by a factor of 64.


The volume increases by a factor of 27.


The volume increases by a factor of 16.


The volume increases by a factor of 9.

Answer 1

Hello!

First, you'll need to find the Volume of each cube. So a cube has dimensions of the same length, so the length, width, and height would be 4 inches for the small cube and 12 inches for the big cube. So you would need to multiply 4 three times.

4*4*4

so 4*4 is 16. Then you'll need to multiply 16 by 4 to get a Volume of 64in³. For the big cube, you'll now have to multiply 12 three times.

12*12*12

So 12*12 is 144. Then you'll need to multiply 144 by 12 to get a Volume of 1728in³. Now you'll need to divide 1728 by all of the numbers that you can choose from. If you divide 1728 by 27, you'll get the Volume of the small cube, 64in³.

So your answer is "The Volume increases by a factor of 27"

I hope this helps!

Answer 2

Calculate this:

volume of larger cube (12 in)^3 (4*3)^3 in^3
-------------------------------- = ---------------- = ---------------------
volume of smaller cube (4 in)^3 (4 in)^3 in^3

(4 in)^3*(3 in)^3
= ------------------------- = 27 The vol increases by a factor of 27.
(4 in)^3